You have to mate with other cats (Duskfall, Dustfeather, Cottonwillow, fallenfeather, or Nightwhisper). The two toms would ask if you want kits if you are a she-cat and the she-cats would ask you if you are a tom. If you want a lot of kits and mates, I recommend being both in this game.
To mate with Fallenfeather, you will have to be a Tom or both. After you are a warrior or leader, talk to her over and over again, then you will be able to ask her. It might take a couple of tries for her to say yes though.