Why does Della sell her hair?

to make the rent payment

to buy Jim a chain for his watch

to buy herself some combs

to anger Jim

Della sells her hair to buy Jim a chain for his watch.

Explanation:

it was Christmas Eve and she wanted to get him something for Christmas the next day, but little does she know Jim was thinking of her too and sells his watch for combs for her hair. (which would be useless now that her hair is short) in the end both characters learn just how far that they are willing to go just to put a smile on the other's face. how sweet <3