One of the features of the Facebook for Developers platform, which makes possible the integration of social networks with many services, websites, games and applications, is an application called Filefly.

Filefly is an application that lets you share files with friends on Facebook, free, in a private, secure and easy to use way. 

At first login you will be asked to create a new folder, then simply click on "Add files" and add the files you want to share. 

Once you have completed the process you can select the friends with whom to share the folder. 

It can share files up to 2GB.