Well, that would depend a lot on what character, role, or whatever. Sometimes, the appearance comes first, and then I realize what role they'd fit in as best. Sometimes, the concept comes first.
I'll use 2 different characters for examples. For Beastling, I was sitting in school, drawing (of course) and I sketched a cutesy little puppy, and then gave him wings. That's where Beastling came from originally. He fit into the worlds I was "building" perfectly, and this comic was born.
For another character, I'll use one you aren't familiar with (though some here may be): Phairon. (Phairon may eventually show up in PE, though that's a big "May" in this case.) Phairon's concept came before he did. He's based very heavily on an ancient god of war and fire by the same name. (Yeah, he came about while I was studying random religions). Accordingly, his story and idea came before the way he actually looks.
Do you see, now?