Above and beyond just averaging the light/reflectance of the scene, matrix may employ some fairly complex things...like color, object recognition etc. As far as I know, the companies like to keep the 'how they do it' pretty secret when it comes to their matrix or evaluative metering mode.
Just as an example, the matrix mode may recognize that you're shooting a person, and thus base a higher percentage of 'importance' on the part of the image where the person is. But it may also recognize how much of the scene is taken up by the person, and this may influence how much importance is given to the person vs how much is given to the 'background'.
Basically, they want it to be a 'smart' as possible, so that people don't have to really understand metering to use it. It's pretty much the 'dummy' mode that shows up in all their cameras, not just the DSLRs. On one hand, it often does a pretty good job. But on the other hand, when the camera is doing the thinking for you, you can expect to get results that you don't expect...if you know what I mean.
Spot metering, on the other hand, will read a specific spot (the actual size of the spot will vary by setting/camera/brand etc.) and it will ignore everything else in the scene.
So for example, if you are shooting a portrait and the background is significantly different than the subject, you will likely see a significant difference in the way that matrix meters the scene vs the way that spot does.
But either way...you need to realize that just because you meter on a specific spot, or take some sort of average of the scene....it's not necessarily going to get you 'proper' exposure. The camera's meter is calibrated to give you an accurate exposure, only if it is reading something that is the same tone as 'middle grey'. We commonly refer to 18% grey as middle grey, but I think camera makers have been shifting that value over the years.
But the point is that if you meter on someone's face...you may still over or under expose the photo (depending on how bright or dark their skin tones are)....unless you adjust your exposure away from the metered value. With a good understanding and enough experience, it's fairly easy to judge how much compensation you need to apply to your exposure.
Another way to do it, would be to use a grey card.
How to use a Grey Card ~ Mike Hodson Photography