Alpha is a byte variable that is often included as the "fourth" byte in a RGB color format. Alpha is an opacity rating from 0 - 255, where 0 is completely invisible and 255 is completely visible. In a VMT file, the "$alpha" parameter is normalized from 0 to 1.0. The value used in the in-game texture is $alpha * 255. That is, an $alpha of 0.7 will convert to a texture alpha of 178 ( 0.7 * 255 = 178.5, floor rounded to 178 ).
To store an individual alpha value in each pixel, an alpha channel is used as the fourth channel of the TGA file. This allows variable opacity, for example, in a single texture, such as the lettered Petrol signs in Half-Life 2. The texture's alpha channel can also be used to define self illumination instead of opacity.