To renounce is to officially give up or turn away from. If you decide to become a vegetarian, you will renounce hamburgers and bacon.
The transitive verb renounce is a stronger, more formal way of saying that you reject or disown something. A prince who's tired of the royal life could renounce his title and become a commoner, and a senator who wanted to become an independent would have to renounce her ties to her previous political party. You'd be wise to heed the wisdom of Jean-Jacques Rousseau, who said: “To renounce liberty is to renounce being a man, to surrender the rights of humanity and even its duties.”