By exposure, it is referring to whether the picture is properly exposed. The camera and lightmeters judges exposure by comparing against the midtone, which is 18% grey. Thus when you adjust the exposure settings, you are overriding the camera's decision and increases or decreases the exposure.
For example, when you are taking a frame with a lot of dark areas, or many people are wearing dark colours, the camera assumes that there are insufficient light and may reduce the shutter speed to allow for longer exposures. The image will end up overexposed. So, to compensate, you can reduce the exposure setting so that the frame will be correctly exposed.
if you're talking about spot, partial, evaluative, center-weighted metering then there should be a button on your cam that allows you to select which one to use.
simpliest way to explain is that each one determines where in the frame the camera will judge exposure from.
so like spot metering, the camera will determine exposure settings from that spot
center weighting..the camera will use the center of the frame more than the edges to determine exposure settings...etc etc
best way to learn when to use what is to read on the internet (i'm quite sure there are good writeups on this floating around) and to play around with it