By spending credits you can play additional matches on each day without regular games. These games - called friendlies - help you to test out special tactics or try out your youngsters performance. Compared to the "free of charge friendlies" you can play each Friday these games are without any public audience, without public stats. Only the match result is viewable to all.
By using the Gamecenter you can watch your matches as they were live. To have the same behavior on matches of other teams you need to purchase "Gamecenter premium", and to do so you need Credits.
To be part of a Friendly Cup you need Credits too, since those matches are played on Wednesdays and Sundays. By the way: both the winner and the runnerup of such a friendly cup earn bonus credits. Check the friendly cup section for more details.
There will follow more options to spend your credits.
Credits can not get transfered to other users.