Inspiration -- well, I don't do a lot of original characters, but I do a lot of original designs--like, a character from a book, where there's maybe a description of the character but not an illustration. So I guess the books that I do costumes from would be my inspiration. Sometimes, like with my recent Mara Jade costume, I'll start with a cover illustration as inspiration but then turn it into something original (since authors almost never have any say in cover illustrations, I don't take those as canon depictions of characters). I usually try to adhere to the book's description but sometimes I'll ignore pieces if I think something else would work better, same as someone might do if they were making a movie of the book.
Backstory -- well, with book characters, they have plenty of backstory.
Why? I read a lot, probably more than I watch tv or movies or read comics, and I find myself attached to the characters, same as I would in a visual medium. Plus well, I like the challenge of trying to create something where anyone who's read the book would recognize me, even if their own mental image of the character had been totally different. I think doing my own designs is more fun that doing a strict reproduction of something, and doing cosplays from books lets me design stuff while at the same time enjoying the experience of dressing up as a character I love.
Currently working on:
Visas Marr -- KotOR II
Al (armor) -- FMA Brotherhood
Mara Jade -- Star Wars EU
Loki -- The Avengers