There are a two ways bans occur in Club Penguin:
1. Automatic bans occur when a player uses inappropriate language that is marked by our security system. These bans happen immediately, and the player will be logged out of Club Penguin, and banned for 24 hours.
2. Moderators can apply bans to a penguin at any time. When a penguin is reported, a record of all conversation, including filtered messages, is sent to our moderators. Moderators review the conversation and will ban accounts found breaking the Club Penguin Rules. Accounts can be banned for 24 hours, 72 hours, or forever depending on the offense.
There is NO way for another penguin to place a ban on your account. Only moderators can place bans.
Read the article Why was my penguin banned? for more information about bans.