Before we go into Gamma let us take a look at what Delta is. Delta predicts the change in the option price based on a $1 move in the stock. So, if the Delta is .5 then the option price will move $.5 for every $1 move in the stock.
But Delta is always changing and that is where Gama comes in. Gamma measures how fast Delta moves. If Gamma is .02 then delta moves up .02 for every $1 move in the stock.
Let us look at an example of how this works. You have a $4 call option with a Delta of .5 and an option gamma of .02. The stock moves up 1 this moves the option to $4.5 and delta to .52. Now if the stock goes up another $1 the stock goes up to $5.02 and delta goes to .54.
These do not give you the exact value of the change in the option but it is a good estimate.
The reason Gamma is important to understand is the same reason why it is important to understand compound interest. As a stock moves in one direction or another the delta increases a little, as that happens each move affects the option even more than it did beforehand.
If you are trying to limit your loss on a stock option and use only the Delta to calculate how much you would lose in a certain situation then you will be surprised when you find out you lost more than you were expecting.
If you just use the delta when calculating your potential reward you might underestimate your return and not get into a perfectly good trade as a result.
Other Option Greeks
Knowing more about the Greeks can help you predict the change in an option which you can use to determine your risk and reward. Here are some more Greeks.
Option Delta - Measures the move in the option compared to the stock.
Option Theta - Measures the role time has on an option
Option Vega - Measures the change in the option due to volatility