This has ben a proverb since the 1600s. It means the person makes no attempt to conceal his/her feelings/emotions, perhaps especially in matters of love. If something is "on your sleeve", it is obviously easily visible to anone who looks at you.
I should perhaps have added above that the earliest recorded use of the words was in a speech by Iago in the opening scene of Shakespeare's Othello. It is interesting that, in this instance, Iago shows emotions he wants to be attributed to him - though they are not genuine - specifically in order to deceive!
That is pretty much the exact opposite of the words' modern meaning.