This is a good question. Della has managed to save 1.87 by being frugal. She tried extremely hard to save every penny where she could. O. Henry writes these words:
"That was all. And sixty cents of it was in pennies. Pennies saved one and two at a time by bulldozing the grocer and the vegetable man and the butcher..."
As to why she was depressed, the reason is clear. 1.87 is not a lot of money for all her effort. Moreover, it was nearly Christmas and she wanted to express her love for her husband, Jim, by getting him a gift. However, she did not have the means to do so. So, she decided to cut her hair and sell it to gain extra money to buy him a chain for his pocket watch. The irony is that Jim also wanted to express his life for his wife, Della. So, he sold his watch and bought her combs for her hair.
In O. Henry's "Gift of the Magi," Della has only managed to save $1.87 towards a Christmas gift for her husband. She is embarrassed that she has had to earn this money through begging and bargaining as suggested in the lines
...bulldozing the grocer and the vegetable man and the butcher until one's cheeks burned with the silent imputation of parsimony that such close dealing implied.
She is depressed because the next day is Christmas and despite her efforts, she still does not have enought money to buy the watch fob and chain for her husbands beloved watch.
In order to purchase this, she realizes she must sell the only possession that she has of value, and that Jim loves most - her hair. She is finally excited to do this, but the ironic twist comes when Jim sells his watch to buy a comb for her hair after she sells her hair to by a fob for his watch.