to be into something means that you are very interested in it. For example (and the following examples are very typical uses of this expression, by the way):
I'm into computers.
This means that you're very interested in the field of computer technology. You have lots of computers at home, you read books about operating systems, programming languages and things like that. In other words, you're a computer buff.
Sorry, I'm not gay. I'm only into girls.
This means that you're only interested in dating girls and not men because you are heterosexual.
Are you into me?
Here, the person probably wants to know whether the other person he or she is talking with has feelings of romantic love for them. Basically, she or he wants to know if the other person likes her or him (in other words, wants to know if the other person is interested in them romantically).
Simply put, I'm into you is a slang way to say I love you.