The Velvet Underground was only together for not that long, they only made 4 albums, but in the time they were together they were changed the game. They were precursors to later movements like punk and new wave; with the album it was very different from what was popular. They were influenced by folk rock in the style of Bob Dylan but with songs like Venus Furs it was clear that they were vastly different and was bringing something that was fresh.
Early on the band was supported and produced by pop artist Andy Warhol and was promoted through shows with amazing light shows like Exploding Plastic Inevitable. John Cale and Lou Reed were the primary songwriters and John who came from a classical background and was held as a child prodigy and Lou came from Long Island and was drawn to avant-garde jazz and rock and roll. He was an intense songwriter who previously worked as an assembly line songwriter. When they got together they made a new sound, Reed brought the abstract sounds like plenty of guitar feedback and unique storytelling while John brought the instrumentation of pianos and bass lines. Andy's vision for the band was to combine the three elements of music, art and film.
This came to pass with them being included in Andy's organization, the Factory, the joining of art and music with them was clear with Andy being a producer on the album and the actual cover has a Warhol print on a banana. Their albums were not commercial successes in a general sense but were majorly influential. The bands U2, R.E.M, Sex Pistols, and Sonic Youth were all heavily influenced by them and Brian Eno was quoted saying that he did not know many people who brought their albums when they were originally released but those who did started bands.
As someone who is in the industry, I can tell you this is truly groundbreaking and I have never heard anything like this with the experimental style. As a listener, I do instead prefer Nico's style and he seemed influenced by Bob Dylan's style of folk music.