The key to understanding Gamma is to first understand that the human eye does not see the world in the way that it truelly is, and as such we don't perceive the world in the same way that a camera does. Even though the camera has a more accurate representation of the real world, it doesn't look right to us because it's not the way we perceive our world. This means that there are things that need to happen to the video signal for it to look accurate to us.
There are two key differences between how our eyes capture light and how a camera does:
1) Less Stops
Human eyes are more advanced than modern film cameras in that we can see a larger amount of stops, worse the monitors we end up viewing the final product on can display an even smaller amount.
2) Data Apportioned to different areas
Humans have adapted to see more detail in dark areas - the theory of course being that we do this because this is where our natural predators hide. The camera has a more objective viewpoint, so where we apportion more data to dark areas the camera sees it as it is.
The difference is linear vs logarithmic.
The video below does a great job explaining this concept and it's very similar to the way Patrick explained it in class:
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