They began operations in 1993 as a result of the 1991 Child Support Act (GB) and Child Support Order (NI). They both operate equivalent legislation for the same purpose, and in fact cooperate and to some degree work-share. They exist to trace the non-resident parent if necessary, to assess how much he (or she) should pay for Child Support Maintenance, to provide a collection service for this money if required, and to enforce payment if required.
If you are prepared to read just one book on the subject, read Child Support In Action. It describes in an approachable manner the political processes leading to the legislation, then the creation of the CSA and its first few years of operation.
Another good book, somewhat slimmer, is Trial and error: a review of UK child support policy. It also looks at some foreign approaches.