"Prince Ami" is what I've been calling Ami since she got short hair and a preview showed her trying to seduce Uta.
Ami had also been hinted at being Bi for quite awhile, with Chika and Maya seemingly being the ones she's most interested in, so I figured something like this may occur eventually, and Otoha had been considered a Prince, which made calling Ami one, appropriate, imo.
Overall: Inside Joke that translates to "Ami is coming for Sensei's Harem."