No problem ^^ I was afraid my English level wasn't good enough for me to explain it clearly and briefly enough, but I'll give it a try.
Cycling can mean two things:
1. After someone lost a villager they really love, they can decide to 'cycle' 16 villagers to get their once beloved villager back. You need to have 16 move-ins and move-outs before you can adopt the villager you lost back in your town. It can take a while.
2. Some people (like me) dedicate an entire town to cycling. Through time travelling, we get a lot of villagers move in and out of our town. We can decide to sell, trade, or give them away. The point of cycling can be to make profit out of it, and/or help people get their dream villagers. In a cycling thread, the user who cycles will warn other users to let them know who moved in, who is 'in boxes' (i.e. moving out and therefore available for adoption)... People may 'lurk' for their dream villagers (also known as 'dreamies'), and the cycler can send them a notification when their dreamie is available.
I hope it helped you n_n