What are cats for?

Solution 1:

I'm just going to quote the civ-clicker's wiki on cat :

Cats are a type of population, which cannot be created by the player directly. They are not affected by the population limit, nor do they consume food.

About creating more :

Each time the player creates workers by clicking a button, there is a certain chance that a cat will be created at the same time. It is irrelevant if the button for 1, 10, 100 or 1000 workers is clicked, the chance of creating a cat stays the same.

They influence at this time 2 thing, as Pest control :

The increase in food production will last 10 seconds * number of cats.

And Warmth of the Companion :

Each cat counts as an additional apothecary, but will not be affected by happiness.

You got 3 achievements when having 1, 10 & 100 cats accordingly.

It seems, according again to its wiki, that more features and builds around cat will pop-up.