Buy, breed and then sell. That's pretty much the just of the game.
Breeding has different levels to it. If you own 2, you can breed them yourself. If you only own one you can either whore out your cat for ETH as a sire ( male ) or you can go to the market place and select a cat to sire with, paying the owner their fee and your cat becomes the mom. The latter I presume you keep the new kitten.
Mechanics wise I think 2 cats bred with specific characteristics will result in a better breed. I read something about this but not sure what it is ( basically to obtain the best kitten possible you must breed certain characteristics together ).
There is also a speed mechanic which relates to the breeding cooldown which once lapsed you can breed that specific cat again. Fast being 2minutes cooldown and then the slowest I think is 1 week. I believe for every time you breed the cooldown increases so thats why fast kittens are more expensive than the slowest ones. Also that is why you should be very careful about just breeding for the hell of it.
EDIT: Don't think of this as an investment because it's not.