Both matrix or average metering modes work in a similar way on entry level DSLRs and they are the easiest of the metering modes to use. In this metering mode your camera’s light meter assesses the whole scene, i.e. everything that you can see in the viewfinder:

The light meter takes it’s reading from an average of the whole scene and tries to achieve a correct exposure in as much of the photo as possible.

In the example below we have some light areas and some darker areas. By using average metering the camera has assessed the whole scene and then done a reasonable job of keeping some detail in the sky as well as exposing the field correctly. We can see detail in the whole photo, nothing is particularly dark or light. The camera has done a good job of exposing every part of the photo well.

Matrix metering can be used well in situations where the light is relatively even throughout the entire photo, such as on a cloudy day. It might give unpredictable results in high contrast situations such as direct sunlight with shadows. This is because the camera will try to average the very bright areas with the dark shadows and neither would be well exposed.

In matrix metering mode you don’t have any control over which area of the photo is being assessed by the camera’s light meter, so you have less control. But, it is the easiest metering mode to used because you don’t have to think about which part of the photo the light meter is ‘looking at’ because it is assessing the whole scene. If you are happy for the camera to make the decision on how the photo should be exposed, then you should use it.