A cycling town is a game file that is solely dedicated to find villagers for other towns, be it for free or for auction. They will usually have threads that announce when a villager can be picked up. There are methods to quickly move villagers out of town, albeit randomly, which is what cyclers will usually use.
Clearing a void means visiting a town with 10 villagers before vising someone else's town. This will decrease the likelihood that a person recieves a "voided" villager which is usually an undesired and unexpected villager.
A cycling town is when someone time travels to rapidly move villagers in and out. Your 'void' is where villagers go when you don't trade them with someone, and just let them move out. If someone visits your town or you visit theirs, there is a chance that a recently voided villager of yours will move to their town. That's why a lot of people ask that you have a clear void before you visit, so they won't get any unwanted random-move ins.
Your void is basically the space on the game that contains the last 16 villagers that moved out of your town but did not go to a new town. Despite what people think, you can't clear it. Your game will still remember them. The only thing visiting a town with 1 residents does is ensure that person won't get a voided villager because they don't have any room, but the void is always there.
