Exposure is the amount of light that enters into your camera.
A photograph's exposure determines how light or dark an image will appear when it's been captured by your camera.
The first photo is an example of an underexposed photo where there was not enough light captured by the camera.
The middle photograph shows a properly exposed photo where there was just the right amount of light captured by the camera.
The third photo is an example of a overexposed photo where there was too much light captured by the camera.
There are three main ingredients to good exposure:
Aperture - is like your pupil, (dilating) getting larger to let more light in) or getting smaller to let less light in.
Shutter Speed - is similar to a blink of an eye. Blink fast and only a small amount of light gets in. Blink slow and more light gets in.
ISO - makes the sensor more or less responsive to light. (think sunglasses)
Each component lets light in or stops light from coming in to your camera in a different way.
Varying any one of these simply makes the resulting photograph either brighter or darker.
Your job as a photographer is to balance them to get the best possible exposure.
In the end, exposure is subjective, there is no right or wrong exposure.
Think of a perfect exposure as a perfect triangle - all the angles are equal, all the sides are equal.
If you increase/decrease the length of one side it is no longer perfect.
You must equally decrease/increase, respectively, the length of another side, or split the change proportionately between the other two sides.