This is the name of the first demo versión of the "Erotica" song we all know. This first versión was composed by Madonna and Junior Vasquez, when Madonna wanted Junior to produce her new album. We don't know the reasong that made her change her mind and ask Shep Pettibone to produce it.
"Love Hurts" is quite far away of the final versión that Shep Pettibone would later do. Nobody has ever heard this demo, and there is no copyright saying that it was really made... but there are some lines of its lyrics which are griten by Madonna herself (or at least this is what it is said). This lines are quite different from the "Erotica" lyrics:
"Sometimes you cross that line - Love hurts - You gotta be cruel to be kind - Love hurts - Tell me whats on your mind - Love things - Love burns - Love sings - Love yearns - But of all love hurts...".
There is also another demo of the first recording sessions from the "Erotica" album, now with new producer Shep Pettibone, called "You Thrill Me".