PG = Propylene Glycol
VG = Vegetable Glycerine/Glycerol
Basically they are inert chemical compounds that used to store chemicals in.. such as flavours, fragrances and in the case of ejuice/eliquid: nicotine. As they don't affect the other chemicals, other than preserving them to some degree, as well as being organic; they are the perfect "medium" for holding flavours and nicotine in a kind of chemical stasis at least to the point of slowing decay anyway.
The main difference, as far as we are concerned, between PG and VG is that VG generates more vapour but, in many cases, decreases flavour; whereas PG increases throat hit without sacrificing flavour. The most common mix I have seen is 80% PG and 20% VG.
There's a lot more to it of course.. but that's the basic idea of it.