Exposure is the control of the amount of light reaching the sensor (or film for that matter) to give a correct result given the ASA used. The meter (and they are tremendously accurate these days in 95% of cases) will give a reading of the given scene and will calculate the required exposure based on the brightness of the scene and the aperture and shutter speed in use (manual) of course we all know that other combinations are now possible, programme (the camera does it all), aperture priority (where you can set the aperture and the camera calculates the shutter speed) and shutter priority (where you set the shutter speed and the camera works out and sets the aperture).
The exposure meters on all DSLR cameras nowadays is a very sophisticated piece of technology but it can still be fooled by extremes of lighting and you need to learn how the meter in your camera will react in certain circumstances and be able to compensate for those extremes to attain an accurate exposure. I call this engaging BRAIN. Your camera's BRAIN is set up to react in certain ways which may not necessarily be what you want, using your grey cells will compensate for the camera's lack of reasoning power.. Learning to see and compensate, is important.
With your camera set to MANUAL you will have to do all the work. Take a meter reading, adjust the aperture and shutter speed to get an accurate exposure and engage the brain to compensate if required. If the meter indicates an overexposure you will need to adjust the camera to a faster shutter speed or set a smaller lens aperture, depending on the subject and what you want to produce in the picture (ie soft background sharp subject would be done with fast shutter speed and large lens aperture).
This mode allows you to adjust the shutter speed and let the camera choose the aperture value automatically. This is useful when you want to capture motion in different ways, such as freezing or blurring it. For example, in sports photography, you might want to use a fast shutter speed to stop the action of the players. However, a faster shutter speed means less light entering the camera, so the camera will try to compensate by opening the aperture more. This can limit your options if your lens has a slow maximum aperture or if you want more depth of field. In that case, you might need to increase the ISO setting to make the sensor more sensitive to light. Keep in mind that no lens performs optimally at its widest aperture, so try to use a smaller aperture (higher f-number) if possible (for example, if your lens has a maximum aperture of f/4, aim for f/5.6 or f/8).
This mode lets you set the aperture value and let the camera determine the shutter speed automatically. You need to monitor the shutter speed and make sure it is fast enough to avoid camera shaking if you are holding the camera by hand. This mode is great for controlling the depth of field, which affects how much of the scene is in focus. For example, in portraiture and landscape photography, you might want to use a large aperture (small f-number) to blur the background or a small aperture (large f-number) to keep everything sharp. (I use this mode most of the time).
This mode lets the camera decide both the shutter speed and the aperture value for you. However, you should not rely on this mode blindly and always check if the exposure is appropriate. You might need to use exposure compensation or switch to another mode if the camera gets confused by tricky lighting conditions.
You are the master of your camera, not the other way around. Take charge and learn how your device works, what it can and cannot do, and when it needs your intervention. ALWAYS USE YOUR BRAIN, it's the best way to get good pictures...