Each dot on your screen must be rendered and textured.
A pixel is a part of a polygon (such as part of a wall or floor etc). Each pixel must be "painted" or texztured to look nice. Most games apply two textures (or more) to a single pixel, one for it's color and one for it's lighting. Hence, many video cards can texture each pixel twice at the same time (to make things faster). Texel referres to this process, since the "effective" rendering speed doubles (since you don't have to go back and apply the second "coat of paint" on the pixel.
For example, a TnT has two pixel pipelines and each pipeline can texture one pixel. OR, it can produce a single pixel with two textures each cycle. A Voodoo3 has only a single pipeline and can apply two texture per cycle.
If the above chips run at 100MHz, the TnT can produce 200Megapixels OR 200Megatexels (200Million), the Voodoo3 can produce 100Megapixels OR 200Megatexels.
A more modern example, the Geforce2 has 4 render pipelines and each can multitexture. Running at 200MHz, it can produce 800Megapixels or 1.6Gigatexels (1600Megapixels).
Giga is a billion.