Mending is the process of flicking the fly line with the tip of your rod to counteract the effects of different currents in a river to achieve a drag-free drift.
An example of mending is where you have a fast current in the middle of the river and a slower seam of current where you are casting from.
So to achieve a drag-free drift, the angler will need to flick a loop of fly downstream once the line has settled on the water. That way the fly and the section of fly line closest to it will drift faster and eventually catch up to the position of the loop.
The easiest way to understand it is to look at the video below.
Mends can be upstream mends, where you flick the line upstream, and downstream where the reverse applies.
A more advanced technique that is really effective is the aerila mend, where you thrown in a mend when the aerialised fly line is just about to settle on the water.
The advantage of this is it doesn’t jerk the fly at all, something which happens a lot with conventional mends..