Sublimation is a printing process invented in the late 1950's but it was only really commercially developed around 20 years or so ago, so it is fairly new and it has only really became a mainstream process for small format use in the last 6-7 years or so..
The sublimation process is quite a nifty way of printing, basically you heat the item up that you want to print (mug, phone case, rock slate etc) with the sublimation paper attached to it and then the ink evaporates at the baking temperature beneath the polymer or polyester layer of the product without it turning in to a liquid.
If you make a mug it is actually dishwasher safe and fade resistant, this is because once printed the ink goes under the outer layer of the actual mug and not on top of it.
To print with this method you would need a heat press machine, a sublimation printer and the relevant software to design your products like Photoshop (also elements) or Corel Draw etc.