An item that Du can 'fan' can be several things here on fanpop: video's, images, Artikel and links. If Du see an item Du like, and Du would like to express that, Du can become a 'fan' of that particular item (similar to the 'like' button on Facebook).
When Du click the green button that says: 'fan of it?', Du become a Fan of that item. Becoming a Fan of an item doesn't have big consequences for you, it just means Du like this item. It can help other users to find good quality content (if a lot of users are Fan of an item, it's probably good quality).
If (for some reason) Du would like to 'unfan' a certain item, do the following: Go to your Profil page. Click on 'Favorites'. Click on 'Content I'm a Fan Of'. Find the item Du would like to stop being a Fan of and simple click on the little red cross.