If something is discouraging, it makes you lose your hope or confidence. A discouraging grade in your science class might make you rethink your plans to become a marine biologist.
The adjective discouraging comes from dis-, "away" or "lack of," and the Old French coragier, "spirit." Things that cause you to lose your spirit are certainly discouraging, from disheartening election results to a difficult conversation with your parents about your allowance. It can be discouraging to watch the news sometimes, and you might need to seek out some positive, encouraging stories to rebuild your spirit from time to time.