My understanding is that a 'circle' is a group of manga or doninshi artists that work or publish collectively. A good example of this would be Clamp, which is a group of manga artists well known for doing the character designs for Code Geass.
The special spot for circles in tagging is thus pretty obvious, since this is a booru site and boorus usually host large amounts of Japanese artwork, some of which is produced by groups rather than individual artists.