One of the things we learned about Girls when doing our cover story on the group is that, though it sounds like it's about an ex-girlfriend, "Laura" is really about a friend. About the song, Christopher Owens, the band's songwriter, says:
“Laura,” is about Laura. It’s directly to Laura. Laura was Liza’s [Owens' ex-girlfriend] best friend, and when Liza and I started hanging out all the time and going out, Laura got mad at me because I was taking her best friend away, kind of. At first, Laura liked me a lot, like, “Oh, he’s great. He’s great.” And then as she realized, “Oh, I’m never going to hang out with Liza now,” then it was like, “Oh, Chris sucks.” So then I’d be like, “Oh, she sucks.” And we had this feud. It’s so juvenile. You sound like 15-year-old girls. It was horrible. But as soon as it was all over, I thought to myself, “You really like Laura.” I think she’s great. So the song is about like, “Let’s be friends again.” Both of us wanted to be friends again, but it’s hard to go up to somebody that you’ve been fighting really hard for two years—well maybe not two years, one year or something—and say like, “I’m sorry, let’s bury the hatchet and be friends.” It’s hard to do that.
So Owens wrote the song and gave it to her as an apology and a white flag. She accepted. That's her in the video, too. Watch it at NME's site.