This is a more modern name for what used to be called Child Maintenance.
Child Support used to be claimed through the Courts, but in 1991 the Government changed the rules and created a Child Support Agency which was suppose to do all this instead.
In fact however it is by common consent one of the most useless organisations on the face of the earth. They frequently get their calculations wrong, and even when they get them right they frequently then don't or can't be bothered to collect the money due.
If you need child maintenance or if you're at the receiving end of the demand for it from the Child Support Agency then seek good legal advice.