Neighbors are primarily Facebook friends who are also playing Cafe World. If you invite them to be your neighbors and they accept, you can help each other progress into the game. All of your Neighbors are shown at the bottom of the Cafe World screen. By clicking on a neighbor you can visit his or her restaurant.
By using the My Neighbors page, which is found in the top menu bar next to the Play! Page, you can invite friends to be your neighbors.