Alpha is an Integer variable that is often included as the "fourth" number in a RGB color format. Alpha is an opacity rating from 0 - 255. Smaller alpha numbers make objects appear more faded whereas larger numbers make objects appear more visable.
0 is completely invisible. 255 is completely visable.
Alpha channels will let you specify individual opacity values for each pixel.
An example of where alpha channels are used can be found in the Combine Forcefields.
Even though parts of the forcefields are visable, other parts are not. That is because the alpha channel is hiding certain parts of the texture.