An Interest Group is similar to a standard Group, but it has an additional option - it allows users on your website to express interest in that group. So while you might have Groups that you organise yourself, you may also have groups where contacts can choose to place themselves within that group, for various reasons - such as to sign up to a focus group, or subscribe to a service. This is where you'd use an Interest Group object.
To set up an Interest Group, first create an Interest Group Set object in the backend. This is where you will be storing your Interest Groups. You don't need to configure the object once you've made it - just make sure you add your Interest Groups under it.
Once you've added the groups themselves, opening one will give you this editor:
The only thing left to do is to fill in the usual Name/Description and add any images and permissions you wish to set. Then that's it! The other step now is to choose where on your site you'd like visitors to register their interest in your groups - that's where you'll set up an Interest Group Manager atom.