What does it means "pet", "for breeding" and "for shows"?

These three expressions denote the quality of a kitten that you get from a cattery.

A for shows kitten is a cat you intend to show in feline expositions. In such case, the breeder will propose you a cat very adherent to the breed standard, having good changes of winning a show (but nobody can guarantee it!).

A for breeding kitten is a cat you will insert into a breeding program. Sometimes, the kitten is not also a good show quality cat: he could expose defects that don’t compromise his health or his beauty but simply the adherence to a certain aspect of the standard. On the other hand, his characteristics are good enough to be transferred to the offsprings.

A pet is a kitten that you don’t intend to show or bred. He will simply become your housecat, a lovely friend to play with, to care of and to love.

For each kitten, the quality will be only decided by the breeder who could add some clauses in order to accomplish to his/her breeding programs.