When you're a musician and you first hear the Velvets, you think, "Wait, you can do that with music?" and at almost the same time you hear how shitty it sounds and realize, "Wait, I could do that with music!". And that's the real meaning behind the Eno quote and the VU's lasting influence.
At least that's my story and the only one that makes sense. However you got there, chances are the Velvets weren't like anything you had heard before. I was 13. I knew the radio, 70s music my dad liked, and the Nirvana - With The Lights Out box set my brother had downloaded on the home computer. I saved up for an 80 gig iPod and started developing my own tastes by going through those ridiculous Rolling Stones 500 greatest lists. Of course Dylan and the Beatles are due all necessary reverence, but before I even listened to it something about a song called "Heroin by The Velvet Underground" stuck out to me. Then I listened to it. Literally my life has never been the same since. I didn't know you could do that with music and it still amazes that you can and they did 60 years ago. I had taken piano lessons and kept a guitar in my room my aunt left at our place, but I never picked it up to try to learn someone else's song until I first heard Venus in Furs and just had to figure out how that sound was made. I've been chasing sounds ever since, and I'm far from the only one. So if anybody needs that Eno quote explained, or to know why their influence is incapable of being overstated, that's it.