Knowing how your metering measures light allows you to manipulate and interpret the results and know when you need to change something.
Your histogram is one of the most valuable tools in explaining the tonal values of a scene. The far left represents pure black, and the far right represents pure white. The horizontal axis is 0-255, and the vertical axis shows how many pixels are in each position of each tone.
The optimal histogram should not be too heavily bunched at either end of the horizontal axis, as this can cause loss of detail in the pure white or pure black. Ideally, the histogram should look a bit like a bell curve, with a peak in the middle and starting/finishing in the far bottom corners. However, the ideal theory is not always able to be put into practice, often the light and shadows do not allow us to expose for a perfect histogram. If you understand that a histogram to densely bunched at either end of the horizontal axis can cause a loss of detail, then you can look to manipulate the settings to allow for that clarity to still come through (changing ISO, white balance, shooting directly into the light, adding additional light to the scene).
Light metering is an additional tool to help prevent the loss of details in the pure white and pure blacks.
Spot Metering only evaluates the light around your focus point and ignores everything else. It estimates a single zone/cell and calculates exposure based on that separate area, nothing else. Spot metering works great for back-lit subjects.
Centre-weighted metering evaluates the light in the middle of the frame and its surroundings and ignores the corners. Use this mode when you want the camera to prioritise the centre of the frame, which works great for close-up portraits and relatively large subjects that are in the middle of the frame.
Matrix or Evaluative Metering mode is the default metering mode on most DSLRs. It divides the entire frame into multiple “zones”, which are then all analysed on the individual basis for light and dark tones. The metering system looks at where you focused within the frame and marked it more important than all other zones.
As with all photography, practice is the only way that you are going to improve and understand your camera more. Luckily with digital cameras, there is no limit to the number of images you can take and with there is no limit to the subjects that you can capture as well.