Despite being 'Gods,' the Cheshire Shards are very weak in power. Incognito can vanish from sight and memories, Introvert can shield himself from the outside world in an impregnable shield of energy, and Charlotte possesses the ability to manipulate candy and other sugary substances.
All of the Shards are actually in a relationship with one another, not being biologically related, and with their mutual mate, the once-wife of The Cheshire Cat. Only Charlotte is openly around and hangs out with people around the world, making friends with others.
It is unknown what race these beings belong to, which is why they are given the umbrella term "God." They all have but two shared characteristics, one, as mentioned above, is that they are here as the result of a Godly entity leaving the universe, and the other is that they can all assume a cat-like form, albeit with somewhat exotic colours; Charlotte is a light magenta, Introvert is a deep violet, and Incognito's is unknown.
As far as it is known, none of these beings have any motivation other than trying to make people around them happy and keep life going easily, and keep the once-wife of the Cheshire Cat happy and unharmed. However, they're failing this miserably.