A forum is a place for your members to communicate, and discuss things without all users having to be online at the same time.
You can spilt your forum into different discussion areas, called categories, within which members can communicate via posts and topics. A member can post a message (a post) in reply to a topic (a particular discussion within a category), or start their own topic, which is visible to everyone in that community. Once read, there is the option to post a reply, which can also be visible to the community.
A forum can come in any size or shape, and be used in many different ways - for general chat among your members or to discuss ideas for your next event. You can limit who has access to the forum via the 'forum settings'.