Arid Archway will return itself to its owner’s hand if you control no other lands when its enters-the-battlefield ability resolves (or if you choose to return it to its owner’s hand despite controlling other lands). It’s almost never a good idea to play it on your first turn.

Desert is a land subtype with no special meaning. It doesn’t grant the land an intrinsic mana ability. Other cards may care about which lands are Deserts.