First and foremost, cosplaying is FUN!
I first got into it when I discovered cosplaymagic.com and saw all the wonderful cosplays on there of my fave anime characters and thought how awesome it would be to be able to wear some of them. You get an incredible sense of belonging, especially at cons and meets, when you see literaly hundreds of cosplayers all into the same things as you are. It makes you more confident also. I'm sure alot of people here felt a little odd on the underground in cosplay on the way to their first expo, but when you get nearer [on the DLR platfom for me] they all start swarming around and the atmosphere is amazing!
Plus, in my oppinion, as well as anime and manga, "cosplay brings you together" [its my wonderful logic
For example, one day when I was out shopping I came across a cosplayer in a Haruhi outfit walking past with a friend. I looked once and did a doubble take. My cousin told me a few weeks back that she saw a Haruhi cosplayer walking round Watford highstreet and to look out for her. [sounds very ominous doesn't it XD lol] So I caught up with them and we randomly started talking about anime/manga [as you do]
And that, comrade, is how you make friends in style. XD