The camera's meter measures the light reflected reflected from the scene in order to set the aperture/shutter speed/ISO parameters of the camera such that the total light read by the sensor is equal to a pre-set value. This value is set by the manufacturer and normally is middle gray (I think 18% gray). The different metering modes simply set the relative area from the scene from which the meter reads the light and averages it.

If the scene is very contrasty, then you may want only the important part of it (say, your subject's face) to be exposed correctly. In this case you will reduce the metered area to cover the subject's face.

In practice, this is done by choosing spot (you don't have this in your camera), center-weighted or partial, in increasing size order.

With Evaluative metering, the camera tries being "smart" and "understand" the scene to chose best exposure.

Note that you can override the default average value by using exposure compensation. This way you can make a dark scene really dark and a bright scene really bright and not let the camera make it muddy gray.