Simplified & non-technical explanation, this is slightly different to how most people explain it so it may help or it may make it worse
The first thing to realise is that the light falling on a scene determines what the exposure should be, the light reflected from a scene varies according to what is doing the reflecting. As camera meters measure reflected light this can cause problems. If you were to measure the light falling on the scene, using an incident light reading, you would not have to worry about adjusting exposure for different scenes which reflect different amounts.
Your camera is taught that all scenes reflect 18% of the light falling on them (Digital cameras may be taught that it is 14% or 12% depending on the camera but I will continue with 18%)
First consider taking a picture of a landscape which, on average, is reflecting 18% of the light falling on it.
When your camera is pointed at the landscape it thinks ' That scene must be reflecting 18% of the light falling on it so I need to set an exposure to suit that light. '
If the light gets brighter the camera thinks ' That scene is still reflecting 18% but it is brighter now so the sun must have come out so I need to reduce the exposure to suit the new brighter light '
If the light gets dimmer the camera thinks ' That scene is still reflecting 18% but it is darker now so the sun must be behind a cloud so I need to increase the exposure to suit the new dimmer light'
So far so good but what about scenes which reflect more than 18% such as snow.
When your camera is pointed at the snow scene it thinks ' That scene must be reflecting 18% of the light falling on it but it is very bright so it must be very sunny so I need to reduce the exposure to suit the very bright light '
This means that, although the camera meter shows the exposure as correct, it has actually reduced the exposure and will cause the white snow to be grey.
A similar thing occurs when you photograph a very dark scene, a black horse for example.
Your camera thinks ' That scene must be reflecting 18% of the light falling on it but it is very dark so it must be very overcast so I need to increase the exposure to suit the very dim light'
This means that, although the camera meter shows the exposure as correct, it has actually increased the exposure and will cause the black horse to be grey.
The histogram will show you what you have recorded and you can can use exposure compensation to get the correct exposure for that particular shot.