It means to be transparent as far as a person's emotions are concerned. Someone who "wears their heart on their sleeve" displays feelings in body language and/or facial expressions.

To let everyone see your emotions, especially affection/love.

This means to display your emotions openly and this phrase may derive from a custom started during the Middle Ages jousting matches. Knights are said to have worn the colours of the ladies whom they loved, in cloths or ribbons tied to their arms.