I've seen it mentioned numerous times but I was unable to find anything that explains what its purpose is. 

It is a substance used to keep some vessel clean from some especially unwanted gases (so even a small residue could have significant effect on the device performance, life or eliability) in the way the getter is let to react with the residues of the unwanted gas.
It could serve to either fini9sh off the evacuation process, or to maintain the atmosphere over life (addressing gases, which could release from the internal structures).

So in an incandescent bulbs the red phosphorus is used as a getter to clean out all waater molecules, in order to prevent the tungsten being transported by the water cycle from the filament onto the glass wall.

In vacuum tubes the getter is used to clean out all gases, but especially oxygen, to prevent from ion bombardment of the inner structures (it cause their degradation, but mainly it cause an unwanted electron emission, what degrade the electrical parameters).

In HID lamp outer bulbs a getter is used to get rid of the oxygen.

Hi yes I am probably responsible for mentioning Getters be it the red on stems of some incandescent. If you see on a discharge lamp an area that is silver that would be the getter also the silver in valves (tubes) The process is to fire a chemical which is held on a tiny frame by applying high frequency electric by a loop which fires the chemical and leaves that silver residue. On tubes that have lost their vacuum the silver turns to white and the valve is useless. hope this adds to Medved's excellent explanation.

I too always wondered what getter was for

Vacuum tubes and VFD display units have these. It is to remove oxygen that would otherwise cause oxidization of lamp parts or other issues. Now they are made of barium but they used to be phosphorus made.

All lamps have slow air leaks around where they are sealed. Getters are a pivotal part in a self ballasted merc or its life would be drastically reduced. One of my westy lifeguards lost vacuum and the getter was totally spent, so it caused the filament protecting the tube when it breaks to fail.