1.
variety, diversity, range
A wide range or assortment of different types or kinds.
2.
variety show
A television program featuring a mix of comedy, talk, games, music, and other entertainment segments. Variety shows are a major genre of Japanese television.
Usage: バラエティ is a loanword from English "variety" with two common uses.
Sense 1 (variety): Often used in the set phrase バラエティに富む (to be rich in variety) or バラエティ豊かな (diverse, varied).
Sense 2 (variety show): バラエティ番組 is a staple of Japanese television. These shows feature comedians (芸人), celebrities (タレント), and other entertainers in comedy skits, talk segments, quizzes, and games. Often shortened to just バラエティ when the context is clear.