Oranges are one of the possible Fruits to start out with in your town. Sometimes, you'll find a Perfect Fruit. (Well, a Perfect Orange) It looks like an Orange with a smaller Orange on top. Plant it, and it may grow into A PERFECT ORANGE TREE!!! :D Anyways, shake a tree with the A button and collect the Fruit that drops(If it shows the tree has Fruit).
Note: I DID NOT create the perfect fruit page, i just linked to it. Hope this page helps a bit!