Well, I always thought, contrary to what DV says in his opening post, that a character actor, first and foremost, would not be a star, but, although he might be well known to the public, usually plays supporting, or even minor roles which could be quite memorable but involved relatively little screen time.

A Senator Geary, for example. A Hyman Roth. Moe Green.

I also looked up a definition, and it said that the roles played by character actors were usually "eccentric or unusual" characters.