Asynchronous multiplayer is when you interact with other players, but not simultaneously: you leave hints and messages, like in the Souls series, make a move that your opponent will respond to later, or compete against their recorded results. It's the feeling of being in the presence of other people without having to adjust to their timing.
You can download games with asynchronous multiplayer via torrent: the filters above will help you choose by language, size, and build type.