Events are asynchronous when they don't happen at the same time. If you pick up the crossword puzzle I started yesterday, we are working on it together but in an asynchronous fashion. Please do it in pencil.
Asynchronous is the opposite of synchronous, which means happening at the same time. Think of “synchronous” as “in synch” and asynchronous as “out of synch.” If we're chatting on the phone, our communication is “synchronous.” We respond to each other immediately and when we hang up, the conversation's over. Email is asynchronous because we respond whenever it's convenient. In some cases this means never, which can be mighty convenient.