An "Ash Catcher" is a piece that catches the ash. Once you 'bowl pops' (your cannabis shooting threw to your bong once it's burnt, if you don't use a gauze), rather than going into your bong, its caught in a the extra piece attached to the top of the stem/downtube, with the bowl on top.

This is an example of a diffuser, G-Spot - Diffuser 14.5 - Online Shop

You can get different sorts, but the aim is always to make the smoke less harsh, and smooth.