It was apparently an earring that he had worn, and he no longer wanted to wear it so it through it down and by his surprise Apollonia caught it.
In the original script, his mother had put it on him (she was drunk and telling him he was so pretty he could've been a girl) and Prince gave it to Apollonia when she gave him the guitar. She threw it back after he hit her. These scenes were cut, but he still throws her the earring at the end, symbolizing that they're back together.
Correction: The scenes where Prince gives the earring to Apollonia when she gifts him the guitar, and when she throws it back at Prince when he hits her, are included in the film.
