It means something which a person resolves to do (is determined to do). It is traditional to make resolutions for the coming year (My New Year's resolution is to exercise more.)
A New Year resolution is a commitment that an individual makes to a personal goal, project, or the reforming of a habit.
Examples; Health improvement. lose weight. Physical exercise. Drink less alcohol. Quit smoking. Social service. Take a trip to new places. Improve education: improve grades, get a better education, learn something