If you are despondent, you are discouraged, very sad, and without hope. If you are depressed, you might describe your mood as despondent.
This adjective is often followed by over or about: He was despondent over the loss of his job. If you want a noun, use the words despondency or despondence. The adjective despondent is from Latin despondens, from despondere "to lose courage, give up," from the prefix de- "from" plus spondere "to promise." The Latin words originally referred to promising a woman in marriage.