What does it mean to be a brony?

There is a difference between being a fan and being a brony(or pegasister). A fan just watches the show and enjoys it, and that's fine. A brony is touched by the show on another level, and therefore, joins the brony community. When you're a brony, friendship truly is magic. You help your friends when they're in need, and stand up against those who try to put you down. You can have fun talking about MLP:FIM, writing fanfics, drawing pictures, RPing, and so much more.
That's what being a brony means to me. :)

Basically what DragonAura said.
Bronies/Pegasisters are really in touch with the show, as they know a ton about MLP and make a bunch of fanart of all sorts, like drawings, music, and fanfics. They talk about it on both internet and real life. Go to conventions like Bronycon and Everfree. Besides, it's not just those. It's believing the true meaning of friendship and happiness. Making friends near or far.