Back to Black came out of nowhere – in a sense. Of course, Amy Winehouse had already released her debut album, 2003’s Frank, but, her voice aside, it sounded more or less like the work of a different artist. Frank was part of a wave of jazz-influenced MOR albums that hit big in the early 2000s. A little braver and moodier than the Michael Parkinson-approved likes of Jamie Cullum, Katie Melua or Michael Bublé, but not so different from Norah Jones or any of the artists that followed in the wake of her 27m-selling album Come Away With Me: a bit of jazz, a bit of neo-soul, a touch of hip-hop about the beats.

The songs on Frank were buffed up by professional writers-for-hire; the woman who sang them signed to 19 Management by Simon Fuller, manager of the Spice Girls and mastermind behind Pop Idol and its umpteen spin-offs. It was advertised in the pages of Living Etc, as if the aural equivalent of soft furnishings, something tasteful and unobtrusive with which to embellish your living room. Winehouse hated it, or so she kept telling interviewers. “I don’t have it in my house,” she informed the Guardian a few months after its release. The best she could manage by way of talking it up was to grudgingly suggest “it isn’t shit”.

Certainly, it could not prepare the listener for Back to Black: nothing about Frank suggested that its creator was going to make a genuinely epochal masterpiece. Something had happened to Amy Winehouse in the three years that separated her second album from her debut: skinny, covered in tattoos, dressed like a cartoon of a 60s girl-group member – complete with a vertiginous beehive modelled on that of the Ronettes’ Ronnie Spector – she was almost unrecognisable. The lyrics of its lead single suggested that whatever had happened wasn’t good – no one pleads with you to go to rehab if your life is in perfect shape – but the music was so ebullient you could easily overlook that.

Her sound had changed as dramatically as her appearance: with Frank’s producer Salaam Remi joined by Mark Ronson, then a virtual unknown, Back to Black offered an update of 60s soul and girl-group pop. Characteristically self-effacing, Ronson has suggested that his primary contribution to the album was keeping Winehouse out of the pub, but in reality his decision to relocate the recording sessions to Brooklyn’s analogue Daptone studios and employ its house band, the Dap-Kings, was a masterstroke.

The Dap-Kings had already spent a decade honing their retro soul style, first backing obscure deep funk singer Lee Fields, then Fields’s former backing vocalist Sharon Jones. They gave the album’s sound a toughness and grit that is usually missing when contemporary producers ape the 60s output of Muscle Shoals and Hitsville USA. The sound chafed against the lyrics’ plethora of 21st-century references and hip-hop-influenced intonation (“I’ll check him at the door / Make sure he got green / I’m tighter than airport security teama”), and against Winehouse’s Sarah Vaughan and Billie Holiday-influenced vocals.

The tension between musical styles was infinitely more gripping than Frank’s clumsy attempts to highlight Winehouse’s jazz chops through scat singing and decorating tracks with samples of crackling vinyl. Moreover, it didn’t sound like a knowing pastiche, largely because Winehouse had dispensed with the hired songwriting help and written a set of songs that were strong enough to bear comparison to those she had been influenced by. You could tell how good they were by the artists they attracted: within months of Back to Black’s release, Prince had taken to covering Love Is a Losing Game on stage. As if to underline the qualitative similarity of Winehouse’s songs and the music that inspired them, Ronnie Spector began performing the title track live amid the Ronettes’ hits.

Understandably, everyone went on about Winehouse’s voice. It was a snappy, ragged, extraordinarily expressive contralto that still carried something of the nasal north London drawl of her speaking voice, perfect for conveying both heartbreak and sass. It dispensed with the usual firework-display theatrics of the modern soul diva in favour of an idiosyncratic, apparently untutored approach to phrasing that lent everything she sang a directness and immediacy. Set against the contemporary backdrop of melismatic oversinging and arch indie rock, Back to Black offered a reminder of what it sounded like to really mean it.

But if the praise that rained on her singing was and is fully deserved, it does tend to overshadow what she was singing. Back to Black revealed Winehouse as a sharp, powerful lyricist, whose writing switched from quietly beautiful – “All I can ever be to you is a darkness that we knew / And this regret I got accustomed to” – to blunt and earthily funny: “What kind of fuckery is this?”. The full horror of the co-dependent relationship that inspired her writing would be revealed in time; but at first it seemed only to have provoked a remarkable outpouring of songs about infidelity, longing and romantic despair, shot through with references to hedonism that always feel nihilistic, never celebratory. There are umpteen mentions of booze and drugs but none to partying or having a good time – only to their ability to obliterate.

Back to Black is an exceptionally forlorn 35 minutes: the closest its mood of self-loathing and hopelessness comes to a resolution is Addicted’s bitter line about how marijuana “does more than any dick did”. But it says something about the skill of her songwriting and the arrangements that it is so easy to listen to. What Winehouse had to say was despondent and troubling, but when her voice soars on the chorus of Tears Dry on Their Own, or the intro to You Know I’m No Good sashays out of the speakers, it doesn’t feel like hard work. Even its bleakest moment, when the title track collapses into a funereal thud and Winehouse keeps disconsolately repeating the word “black”, comes wrapped in gorgeous vocal harmonies and strings.

A rare instance of critical acclaim chiming with public taste, it sold millions. It may well be the most influential album of the last 20 years. The immediate effect of its success was a wave of artists obviously working in her image. Female vocalists made retro soul-influenced music, replacing Winehouse’s troubled unpredictability with something less volatile and more marketable: earthy everyman good humour or cute kookiness. Adele was by far the most successful, but at one point there seemed to be dozens of them, all filling the void created by the fact that Winehouse was increasingly unable to play live, let alone complete another record (as the posthumous Lioness compilation revealed, she recorded virtually nothing in the final years of her life, taping only two songs for a projected follow-up). Winehouse’s vocal style became a kind of all-purpose pop template, its idiosyncrasies reduced to a series of slurred, prematurely aged tics intended to signify emotional authenticity. Nearly 15 years on, you still can’t move for twentysomething men who sound like ravaged blues shouters and twentysomething women trying their best to channel Billie Holiday.

Facebook Twitter Pinterest Something happened … Amy Winehouse playing the V Festival in Essex, in 2008. Photograph: James McCauley/Rex Features

And Back to Black ushered in a new vogue for soul-baring albums rooted in the artist’s lives: an updated version of the early 70s trend for confessional singer-songwriters, rebooted for the age of social media, with its oversharing late-night posts and belief that rock and pop artists should be #relatable (Facebook opened to everyone over 13 with a valid email address four weeks before Back to Black’s release; Twitter’s tipping point came five months later). For better or worse, we currently live in a pop world that Back to Black unintentionally helped to create, where writing frankly about your personal experience is the most noble occupation a pop star can pursue; where artists are queuing up to tell the world about the neuroses and trauma that inspired their latest work; where everyone from Drake to Taylor Swift to Beyoncé has their songs pored over for IRL references.

Whether that is a positive state of affairs is moot: the quality of Back to Black isn’t. Untangle it from its legacy and the appalling backstory of its songs, and you are left with an astonishing album – an unexpected, unprecedented burst of creativity and talent that still hits home emotionally, no matter how many times you hear it. It feels impermeable, the kind of album people will still be listening to and talking about for decades to come: the 21st century’s most obvious candidate to join the pantheon of all-time classics.

• Read our obituary of Amy Winehouse