Why do my drains gurgle? How does a CCTV drain inspection work?

your drains gurgle because they are blocked .  

A CCTV drain inspection is a camera  with lights on a 5mm diameter fiberglass rod which is pushed up the pipe  

The gurgling PROBABLY means there is gunk built up on the walls of the drain.

CCTV inspection, means the have a camera on a flexible line that they feed down the line so they can SEE what is inside the drain. Once they know what is in there, and exactly where, they can determine what to do about it.

possible partial obstruction. a very [tiny, really] tv camera on the end of a length of cable is put into the drain -- likely in multiple places. the plumber watches on a tv type screen for problems

You may have a partial blockage, or a collapsed drain, or the design of the system (or any subsequent alterations) may be faulty. A lot of issues arise when larger diameter pipes run full-bore, but many are easy to resolve especially if you know where they are happening.  A cctv survey is simply a wee camera on a probe that allows inspection of the inside of the drain run, which is displayed/recorded on a laptop which helps you find the problem.