Oshi

is a Japanese slang term used mainly for idols and actors, and refers to a person who is your favorite and that you focus most of your support on. It can refer to an individual celebrity or a specific member of a group. It doesn't specifically have anything to do with anime and manga, but often comes up since idols and actors are a frequent topic.

Oshikatsu
, also called, is a term for any efforts to promote your idol or show your loyalty to your idol.