Here is an article from The New Atlantis written by cosmologist Luke Barnes about one specific example of cosmic fine-tuning. (H/T Uncommon Descent via J. Warner Wallace tweet)

Excerpt:

Today, our deepest understanding of the laws of nature is summarized in a set of equations. Using these equations, we can make very precise calculations of the most elementary physical phenomena, calculations that are confirmed by experimental evidence. But to make these predictions, we have to plug in some numbers that cannot themselves be calculated but are derived from measurements of some of the most basic features of the physical universe. These numbers specify such crucial quantities as the masses of fundamental particles and the strengths of their mutual interactions. After extensive experiments under all manner of conditions, physicists have found that these numbers appear not to change in different times and places, so they are called the fundamental constants of nature. These constants represent the edge of our knowledge. Richard Feynman called one of them — the fine-structure constant, which characterizes the amount of electromagnetic force between charged elementary particles like electrons — “one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man.” […]A universe that has just small tweaks in the fundamental constants might not have any of the chemical bonds that give us molecules, so say farewell to DNA, and also to rocks, water, and planets. Other tweaks could make the formation of stars or even atoms impossible. And with some values for the physical constants, the universe would have flickered out of existence in a fraction of a second. That the constants are all arranged in what is, mathematically speaking, the very improbable combination that makes our grand, complex, life-bearing universe possible is what physicists mean when they talk about the “fine-tuning” of the universe for life.

Atheists, both rank-and-file and expert, almost universally misunderstand the fine-tuning argument. They imagine that if the constants and quantities specified at the origin of the universe were different, then humans would just have green skin, or maybe forehead ridges, or pointy ears. Atheists tend to get their view of science from science fiction in novels or television or movies. Just this week I was talking to an agnostic woman (who since reverted to atheism) and brought up the fine-tuning argument. And she said “well, maybe if the initial constants and quantities were different, then we would have evolved differently”. No, the whole point is that life of any conceivable kind becomes impossible if the constants and quantities are altered higher or lower. Even slightly. It’s not that you have green skin, pointy ears, and forehead ridges. It’s that you have a universe that recollapses into a hot fireball, or contains only hydrogen, or does not form stars and planets at all.

I got the impression that she hadn’t read anything about the fine-tuning from peer-reviewed scientific publications, but had just read popular responses to it from atheists with degrees in English and drama and philosophy. If you want to understand a scientific argument, then you have to go to the scientific publications, and read the science. Here is an excellent start, from two astrophysicists, and published by Cambridge University Press.

So what does the scientific evidence actually show?

Barnes explains:

The strong nuclear force, for example, is the glue that holds protons and neutrons together in the nuclei of atoms. If, in a hypothetical universe, it is too weak, then nuclei are not stable and the periodic table disappears again. If it is too strong, then the intense heat of the early universe could convert all hydrogen into helium — meaning that there could be no water, and that 99.97 percent of the 24 million carbon compounds we have discovered would be impossible, too. And, as the chart to the right shows, the forces, like the masses, must be in the right balance. If the electromagnetic force, which is responsible for the attraction and repulsion of charged particles, is too strong or too weak compared to the strong nuclear force, anything from stars to chemical compounds would be impossible. Stars are particularly finicky when it comes to fundamental constants. If the masses of the fundamental particles are not extremely small, then stars burn out very quickly. Stars in our universe also have the remarkable ability to produce both carbon and oxygen, two of the most important elements to biology. But, a change of just a few percent in the up and down quarks’ masses, or in the forces that hold atoms together, is enough to upset this ability — stars would make either carbon or oxygen, but not both.

It’s very important that theists are well-equipped to explain how individual cases of fine-tuning work. We need to know what you lose if you alter these constants and quantities even slightly. You can read about some more examples in this previous post.