It means to empty out any Villagers who moved recently from moving in to the next available player's town they reach. This is done simply by visiting another player's town. Mine would be ideal because I have 10 villagers, so when Greninja would visit my town, his/her previously moved villager would "try" to move into mine (You don't see this, this is a game process.) but since my town is full, the villager just ends up being 'deleted' or cleared. If you want an example, Greninja had Fauna move out 2 weeks ago. Greninja hasn't played with anyone since then. Greninja decides to come over to my town. If I had less than 9 villagers, there's a chance that Fauna would move to my town. (The chance being, my game hasn't already had a villager in reserve to move in.) So after Greninja leaves my town, Fauna is cleared from his/her game. That is how one clears a void.
PS. If you need to do so, I could help if I'm around.