Dean McIntyre offers some basic information on music licensing for churches. It's more complicated than you can imagine.
CCLI licenses only cover copying and projecting of song lyrics, and in limited instances, recordings. However, if your congregation sings in other venues or during events outside the regular worship service, you need to have a separate performance license in order to use music. Dean McIntyre, director of music resources for the General Board of Discipleship, offers information about performance licensing.