From my experience in making wine with my Dad and my Uncles the degassing was to rid the wine of excess C02 because it was coming out "fizzy" like a young cheap wine.
What happens is that the C02 production slows to the point of bubbling at intervals longer than 15 minutes. The pressure in the headspace is the same on the wine below as the liquid in the airlock above so some of the C02 ends up absorbing into the wine.
You can stir the wine vigorously for a couple of minutes with a wooden dowl or a long plastic dowel (just take one of those long plastic stirring spoons used for wort and use the handle end which usually fits into a carboy) and replace the airlock for 45 minutes or so and then do it again until the wine stops bleeding off the excess C02.
There are some cool drill attachments available at LHBS for this purpose and they work better than the inverted spoon. They fit like a bit into your drill and have some little blades (plastic) that flip up when you hit the bottom of the carboy, or when you press the drill trigger and let 'er fly!
Once you've completed degassing, you should let the wine sit for about 8 to 12 weeks. The wine gets flat after degassing and needs time to recover and re-build it's complexity.
I imagine the same process would be used for mead.
Cheers,
Oskaar