Dishonor is a state of shame and disgrace. If you were caught lip-syncing to a recording during a singing contest, you’d probably feel a sense of dishonor.
Honor has to do with respect, so dishonor involves a lack of respect. If you dishonor something, you’ve brought shame to it. Athletes who cheat during a game have dishonored themselves and their teams. You can also say a shameful act brings dishonor. When a politician is involved in a scandal, it brings dishonor to his or her reputation.