The phrase means that you show your romantic interest in someone in a way that others can observe - lingering glances, keeness to strike up a relationship, and so on. The phrase dates back to the Middle Ages when knights in a jousting contest would ask the high-ranking lady watching, often the daughter of the king or nobleman in charge, for her 'favour'. This would take the form of a scarf or handkerchief, and the knight would use it to declare his interest in the lady be going into the contest with this symbol of his affection - his heart- tied on his sleeve for everyone to see.