Fans determine how many people show up in your stadium when your team is playing a match. This becomes very important when your sponsor income no longer is enough to pay the wages of your players and maintenance of your facilities

The amount of fans you have is reflected in your popularity. You can see the popularity of all teams in your league if you click the "clubs" tab in your league overview.

Your popularity increases over time, especially when you play matches. It's not important to win all your matches, but you should try not to lose home matches if you want your fanbase to grow as fast as possible.