For social clubs
Social clubs exists to gather people of similar social interest under a single umbrella. It is sometimes called a cooperative society. Using a .CLUB domain for your social club name will allow you to have a shorter address and since club is in most cases usually included in the club name. The .CLUB will be perfect for such things.
For soccer, football, basketball clubs
When it comes to soccer football or basketball the word team and club are usually interchanged when qualifying them as a group. So using a .CLUB extension for your sport club is another way of showing how unique you are.
For night clubs
Night clubs are places where people go to let losses and be cool at night especially on weekends. Using a .CLUB domain name for your night clubs business page will just being out that spark that will attract people to it.
For various college association, fraternity and groups
In college and high school there are clubs that caters for various class of student interest. Be it science, press, literature etc there is definitely a group catering for that interest. Attract more members to your group through online advert and from your group website registered with a .CLUB domain zone.