Your fanshop increases the popularity of your team. This makes it a very important building since match attendance can become an important source of income for your team.
You can build a fanshop as soon as you've upgraded your stadium to level 2.
The fanshop offers you an overview of the amountof each type of fans your team has. It also offers daily reports of the changes in your fanbase. This will give you insight in how your fanbase changes and why.
Before you have a fanshop you get a daily increase of 100 casual fans. The fanshop increases this amount, giving you a faster increase in popularity.
The fanshop also converts fans to a better type of fans. Casual fans are converted to normal fans and normal fans are converted to fanclub members. The higher the level of your fanclub, the faster fans are converted. This not only increases the likelyhood of them coming to your stadium but also increases the time they stay a fan of your club.