Metering is metering how much light there is. The different metering modes on your camera decide exactly how the camera meters the light (so that it can get proper exposure). You can meter the entire scene, only the active focus area, etc. Your camera's manual will explain each mode in more detail.
It affects how the camera will expose the image, or more precisely, what areas of the image the processor will take into consideration when deciding on its aperture / shutter values.
Spot metering means that its using only a small spot of the frame to determinate exposure
Centered weight average is a bigger area and it takes the average of what it sees in this area.