Katie and her mother Kaitlyn only appear randomly after you visit someone else's town or someone visits yours
Katie and Kaitlyn are two cats that are seperated. If you reunite them you either will get a picture of one of them or a special gift. Katie will follow you around until your friend opnes their gates and Katlyn sees her. You will recieve a present for finding Katie but your friend will not even though they helped find her.
In New Leaf, Katie appears all grown up and travelling the world. If you wifi with someone, there is a chance that she will show up in your town. She will wander around for a while before eventually leaving, but you can invite someone over and they can ask her to come to their town.
These are the gifts you get (in Wild World):
Portrait (just a picture Katie drew with her crayons)