The conversion of UV light into the glowing you see is due to the conversion of radiation into light of the visible spectrum by compounds known as phosphors. This is ofcourse the main technology involved in how your CRT television works, and why white clothes also glow.
Look it up if your interested, though, it is not actually the white t-shirt which contains the phosphors..
The chemically inclined will know that most man-made colours come from using metals known as 'transition' metals, in order to form wave-length changing effects in white light to cause colour. To varying degrees, they are all phosphors, and react to radiation of all kinds.. But hey, if your snakes glow, rock on..