A drag system is a system that creates friction in the fly reel, in order to slow the rotation of the spool in the reel. The purpose of this is that when a fish takes off and is pulling off line, the drag acts as a 'brake' to make it harder for the fish to pull the line off, helping you tiring and eventually landing the fish.
To create this drag, there are 2 different drag systems that a reel can have: a click drag or a disc drag.
A click drag is a system where a pin clicks in a cog in order to create drag. You'll easily recognize a click drag by the clicking sound that it makes.
For fish that do not fight hard, a click drag is often sufficient. It's a more simple and affordable construction, so if you don't need a lot of 'braking power' this is great choice.