An object that's neighboring is right next to something else. Neighboring countries share a common border, and neighboring cars are parked side-by-side.
In a restaurant, if someone at the neighboring table starts telling terrible jokes, you'll have to listen, since they're adjacent to your table. And if you live in Maine, New Hampshire is the only neighboring state. The adjective neighboring comes from the verb form of neighbor, which is rooted in the Old English words neah, "near," and gebur, "dweller."