PBEMs are very similar to tabletop games except that the medium used for the game is email - rather than sitting around a table talking. As you can imagine the timeframes involved in PBEM games are much longer than for tabletop game: A player must write an email, send it, and wait for the reply to see what happened which might take hours or days, whereas in a tabletop game it would take seconds or minutes.
There are many different variants of PBEMs; generally there is a variant for every type of medium used to host the game. For example:
Honor's Hand is actually a PBDG not a PBEM, I called it a PBEM because that term is better recognized and there isn't too much of a difference.