Variety is a radio format that plays music across numerous genres.
These stations tend to favor older listeners and play a mix of music that focuses more on older mainstream music, although much broader than the typical suburban oldies or classic hits station; a full-service station will often play music from the adult standards, classic country, adult contemporary or ethnic formats as well.
Full-service radio also regularly includes room for local news and talk.
Adult Contemporary and similarly formatted stations often brand with "mix" and "variety" to demonstrate the fact that they play music from several decades.
The phrase "variety hits" is a synonym for the adult hits format (typified by the "Male First Name FM" branding), which indeed usually has a larger variety than a typical hot AC station.