How Lyft profiles works is pretty simple. Once it's live, you'll have the option to fill out a profile with your favorite music, your hometown and "other fun facts." The driver can share the same information, with the thinking being that you'll be able to spot similar areas of interest and start up a conversation, or even just agree on what music to listen to. In addition to the basic profile, you and your driver can also user Facebook Connect to share your friends list. This won't randomly show all of your friends to a stranger, but if you do have a friend in common, the app will let you know. Apparently, one in 10 rides would feature a match.
Lyft profiles are optional. You can choose to go all-in, just share your profile and not your Facebook friends or ignore the feature entirely. It seems like it would definitely be useful if you're alone on a long ride across town, but there are definitely times when you've been working for 12 hours straight and probably don't want to talk about what an amazing coincidence it is that your driver knows your second cousin. There's also something to be said for knowing more about your driver, especially given the issues Uber is having abroad.
At launch, the features you've just read about are only coming to the iOS app, with Android "soon to follow." Lyft says this is just the start for profiles, and it'll be adding more features over time.