You can accept a certain number of favors at a time. This information is specific to your level and the level of your castle and can be obtained in the Info tab. Click on a favor icon to see that favors rewards and the amount of time it will take to complete it.
Any building on your flotia that has the favor icon beside it in the Shop menu can have a favor requested on it by friends. Where the favor icon is above a favorable building, there will be a picture of the requesting friend's icon. Click this and click accept favor to accept the request.