A little info on mattes:
Mattes are from film making. When you wanted to do a composite for a film, you'd start by making a black and white film (the matte). You'd put black anywhere you wanted to hide something from the original film, and white where you wanted it show. If you wanted to make something partially transparent, you'd use a shade of gray. If you held up the B&W matte film, you'd see that the white areas are transparent, the black are opaque, and the gray areas partially transparent.
Then you'd take the original film and the matte film, layer them together, and project the result onto a new film. Anywhere that was black on the matte would prevent the original film from showing through. The result is a 3rd film that removed unwanted things from the original.
To make the composite, you'd repeat this process with the other films to be layered together. In the end, you have 2 or more films that had regions keyed out (black). Then you'd take these films and project them together onto the final film. The black areas on one film would be filled in with material from the other films.
You can still find mattes in use today in film, except instead of optically masking out areas the film and mattes are processed electronically.
For video, the reason for using mattes instead of alpha channels is simple; it's very easy to manipulate a B&W image to control the transparency. No special format is required. You can edit the matte using the same tools in the editor that you use for the original video. This makes manually editing or cleaning up a matte much simpler.
One thing I've done for titles is to use a simple B&W title from TDK, put it onto the matte track, and then put the 2D editor on it and animate the title position. This gives you a title that moves across a background video while scrolling over a second video that plays in the title. It doesn't require any special titling software, and previews in real time even on a low-end system.