Vindicated means "freed from any question of guilt." If people think you did something wrong, you dream of being vindicated, or found innocent.
The word vindicated, which comes from the Latin word vindicatus, originally meant "to avenge or revenge" but its meaning soon shifted to "clear from censure or doubt, by means of demonstration." When you are vindicated, your name is cleared. You might also prove that you're right about something. "I told you so!" can be the victory cry of the vindicated.