DIY is short for Do It Yourself. It refers to a type of cube (almost always the 3x3) that comes disassembled and requires the buyer to put the pieces together and place the stickers on the puzzle. Many people claim that DIY cubes turn better and are of better quality than store-bought cubes, and in fact most of the top 3x3x3 solvers in the world use DIYs. One definite advantage that DIY cubes have is the ability to adjust the tightness of the center springs - store-bought cubes usually have glued centers, so it is impossible to change their tightness.
There are about ten different types of DIY cubes, as well as a large variety of different colors. The best place to get DIY cubes is probably cube4you, although if you count shipping they may be cheaper from some vendors in your own country. It is also possible to get DIY cubes from eBay. For a list of the types of Chinese DIY cubes, see the List of Puzzle Manufacturers.