A moderator is there to help the model during their broadcast by monitoring the chats. They are there to help encourage viewers to use the site page correctly and tip when needed. They often help new viewers with the rules of the site.
They will have the same power to ban, silence or ignore you and your chats as the model does. This is because at times the model is busy with her show and doesn't have time to keep a check on all the chats.
These are the types of bans that can be made:
Ignore - Cherry.tv hides your messages.
Silence - You are stopped from sending messages for six hours.
Ban - You are stopped from watching that model's shows permanently. This is irreversible.
That's all you need to know about moderator bans.