When you first set up Apple Music, your account automatically follows artists on Connect if you've purchased their music in the iTunes Store. Connect is sort of like a social network that artists can use to "connect" with fans.
That can be nice, but chances are you don't want to be following some random artist you bought a single from five years ago. To unfollow artists, head over to the "Following" section of the account window.
Once you unfollow an artist, their content won't show up in the Connect section of Apple Music.