Henrietta Lacks, a 31-year-old mother of five, died of cervical cancer on 4 October 1951; and while her disease was a tragedy for her family, for the world of medical research – and beyond that, every one of us on the planet – it was something of a miracle.

Because, in the years since her death, Lacks's cells – taken from her tumour while she was undergoing surgery – have been responsible for some of the most important medical advances of all time. The polio vaccine, chemotherapy, cloning, gene mapping and IVF: all these health milestones, and many more, owe everything to the life, and death, of a young mother.

Lacks's cells – known as HeLa, using the first two letters of each of her names – became the first immortal human cell line in history. Scientists at the hospital where she died, Johns Hopkins in Baltimore, had been working for years to try to start a continuously reproducing cell line – but the cells always died. Lacks's were the first that "took", introducing a constantly reproducing line of cells that are literally, to give them their scientific definition, immortal. (Ordinary cells taken from a human body and kept in a lab have a limited life span; however, an immortal cell line is cultured in a particular way so it has the ability to proliferate indefinitely.) Quite why hers were the cells that survived and reproduced, when those of hundreds of other patients had died, is unclear – but the best guess is that the reason was linked to the ferocity of her tumour, which seems to have been made more virulent by the fact that she also suffered from syphilis.

As soon as it was clear that HeLa would continue to reproduce, all kinds of research and experiments suddenly became possible. For a start, having living cells available outside the human body meant doctors could watch cell division taking place, and could also see how viruses behaved inside the cells. What's more, it was possible to expose the cells to conditions that wouldn't have been ethical if they were inside a human body – for example, doctors could bombard them with carcinogens, and watch the results.

In the years since 1951, HeLa cells have been exposed to endless toxins and infections; they've been zapped by radiation, and tested with countless drugs. And all this – and much, much more – has led to hundreds, if not thousands, of new pieces of knowledge, and helped to shape the way medicine moved in the second half of the 20th century and the first decade of this one. And there are certainly plenty of HeLa cells to go round, these days: one researcher has estimated that if you laid them all end-to-end, they'd wrap around the planet at least three times.

No one would be more surprised to know this than Lacks (who, in her lifetime, stood about five feet tall). But for decades, while HeLa cells were routinely being used in laboratories around the world, and were being hailed as pivotal in breakthrough after breakthrough, no one seems to have stopped to think about the person behind them. Then, 37 years after Lacks's death, a 16-year-old schoolgirl called Rebecca Skloot was sitting in a biology lesson when her teacher explained how cancer begins, and said the process had been learned from studying cells in culture – HeLa cells. The cells, said the teacher, came from a woman called Henrietta Lacks.

When the class was over, the other students filed out – but Skloot hung around. "I said to my teacher: who was this woman Henrietta Lacks? Where was she from? Did she have any kids? But all the teacher knew was that she was black, and that she had died in 1951 from cervical cancer."

After school, and a degree in biological science, Skloot, who is promoting her book about what she calls the "immortality" of Lacks, devoted herself to finding out the truth behind the HeLa cells – and what she uncovered was a tale that is immensely moving. It's also a story that has captured the public imagination: since its publication in February in the US, Skloot's book has never been off the New York Times bestseller list.

What Skloot found out puts the American healthcare system, and beyond it scientists everywhere who depend on patient goodwill, but fail to communicate effectively, in the dock. Because what she found out was that, while Lacks's cells were changing the face of modern medicine, her husband and children not only knew nothing about it – they were also without adequate healthcare themselves. "What most people are most shocked at is that Henrietta's cells were taken without her knowledge, and without her consent," says Skloot. "But that's standard practice, here in the UK as in the US. If you sign a general consent form before surgery, any sample cells removed may be used for research later, and the doctors don't have to let you know.

"The general standpoint of medical science is that cells taken from an individual and used for research benefit the common good, so it's OK to use them. But the Lacks story shows that isn't true – certainly not in America, anyway. Because Henrietta's cells were used to develop medical treatments – but those treatments were only available to people who could afford medical insurance, and impoverished families like the Lackses were exactly the sort of family who couldn't."

To make matters worse, Lacks's cells were making some people – pharmaceutical companies – rich. More specifically, cell banks and biotech companies were retailing vials of her cells – the current going rate for a tube of HeLas is around US $260 (£174). But not a penny of the profits her cells had helped to generate went to her descendants: and while their mother's cells were soaring to worldwide scientific acclaim, fortunes in the Lacks family had plummeted.

It wasn't, of course, all that surprising. The Lacks family were not, and are not, wealthy. Henrietta's husband Day (with whom she'd had her first baby aged 14) worked in a steel mill in Baltimore, making about 80 cents an hour. Life in their household was tough enough, with five children to feed, even before their mother got cancer. What chance, really, would they have with her gone? Skloot's testimony – and she has interviewed hundreds of people for her book – reveals a tragic tale. Lacks clearly knew how precarious her kids' lives were going to be once she wasn't around any more. As she was dying, the doctors told her husband that she was too ill to have visits from her children – the youngest of whom was just 13 months old. So instead, Day Lacks would take them to play in a garden across the road from her ward. And despite being in excruciating pain, Lacks would drag herself out of bed to the window, and press her face against the glass looking at the children she knew she'd never hold in her arms again.

Her last request to Day, Skloot discovered, was to ask him to "take care of them kids . . . don't let nuthin happen to them". And Day tried his best, but the odds were stacked against him. Their eldest daughter Elsie, who had developmental problems, was already in the Hospital for the Negro Insane, and died there soon after her mother. A son, Joe, dropped out of school and later stabbed another boy, and was sentenced to 15 years in jail. Daughter Deborah was a teenage mother who later left her husband after he beat her up. By the time Skloot caught up with them all in 2000, nearly every one was in poor health: Day had prostate cancer and asbestos-filled lungs; one son, Sonny, had a bad heart; Deborah had arthritis, osteoporosis, nerve deafness, anxiety and depression. None had medical insurance cover and money for treatment. "If our mother is so important to science," another son, Lawrence, asked Skloot, "why can't we get health insurance?"

It was Lawrence's wife, Bobette, who was the first member of the Lacks family to hear about Henrietta's cells. By chance, she had met a cancer researcher – and when she told him her name, the researcher remarked that he was working in the lab on some cells that came from a woman named Henrietta Lacks. Bobette said that had been her mother-in-law's name – but it couldn't be her because she'd been dead for years. And then the researcher explained that the cells had been growing for years – ever since 1951, in fact.

It was a crass way for her family to find out what had happened to Lack's cells, but in fact they would have found out anyway. The cell line had been contaminated, and scientists realised they needed to test Henrietta's descendants to work out what had contaminated them. "But when they came back to take cell samples, they didn't explain properly to the Lackses what was going on," says Skloot. "Henrietta's children thought they were being tested for the cancer that had killed her . . . Deborah waited for months thinking she was going to find out whether she'd die the same agonising way her mother had."

One of the biggest issues her book raises, says Skloot, is how important it is for doctors and other health workers to communicate effectively with patients and their families. "If you spoke another language and you needed to see the doctor, you'd be provided with a translator – but if it's the science you don't understand, there's no one there to translate for you, so you go away simply not knowing what's been said. I think there should be science translators, who are trained to communicate complicated medical stuff in a straightforward, easily digestible manner. It would have made a huge difference to Henrietta's family." In many ways, Skloot became the "explainer" the Lacks children so desperately needed. "Usually when you're working as a journalist you're asking people about their story – but when I met the Lacks family, I was telling them about theirs," says Skloot.

Another question her book raises – and it's likely to be even more pertinent in the future, as medical research becomes a bigger and bigger, multi-billion-pound industry – is how much right do we have over the raw materials of our physiology? What rights do the providers of the original sample – or their families – have if their cell lines are later found to be worth patenting?

But the biggest point Skloot wants to make is that behind every test-tube of cells there lies a real, human story. "Tissue is so often dehumanised – it's referred to in medical reports and documents, and no one ever seems to remember that for every single biological sample that's used in any laboratory, anywhere, there's a person." Perhaps surprisingly, she says the people who most conspire to make this the way it is – the very scientists whose experiments require human cells and tissue – have greeted her book favourably. "One researcher said he'd never thought about the person behind the cells and now he knows the story, when he's working on HeLa cells he feels there's a ghost in the lab – the ghost of Henrietta."

Meanwhile in a cemetery in Virginia, where Henrietta Lacks was buried in an unmarked grave, a memorial has at last been erected. It is dedicated to the memory of a woman who, it says "touched the lives of many"; and no truer a sentence has ever been inscribed.

• The Immortal Life of Henrietta Lacks is published by Macmillan, price £18.99.

• Science Weekly podcast: Rebecca Skloot describes the extraordinary living legacy left behind by Henrietta Lacks at theguardian.com/science