When a villager leaves your town and doesn't get adopted by another player, they enter "the void". The villager exits "the void" once another villager leaves your town (into the void or gets adopted).
While a villager is in the void, another player can visit your town and then the villager that was "voided" might move in to the visiting player's town (this is not guaranteed, though).
A lot of players one these forums don't want to have your "voided" villager move into their towns, so they often request for other players to have a "void".
To clear your void, you have to visit a full town (a town with 10 villagers) or the voided villager needs to have moved into another visiting player's town.
Hope that clears things up for you!!