Damon doesn't want to leave Mystic falls but he also doesn't want to be in love with Elena when she choose Stefan, Damon ask a witch to put a spell on him to make him stop loving Elena.
she puts the spell round his heart so no love can get through it but the spell only last a year and only the person who loves him with all their heart can break the spell.
At the end of the story Damon is staked in the heart and the spell around his heart is the only thing that saved him as nothing could break the spell.