Delta isn't necessarily constant across strikes or expirations. Just as Delta represents the change in premium as stock price changes, Gamma represents the change in the Delta for an option as stock price changes.
Similar to Delta, Gamma is given as a number between 0 and 1. The Gamma number is added or subtracted to the Delta as the price of the underlying asset moves. As with Delta, it is figured versus $1 move in the price of the underlying asset.
Assume that the current stock price of IBM is $151.50.
A call option for the 152 strike might have a delta of 0.40 and a gamma of 0.20, while its price might be $1.00. If the underlying stock price goes up $1 to $152.50, we know from delta that the expected new option price will be $1.40. And now we know that gamma dictates that the expected new delta will be 0.60.
Now the option will increase $0.60 for every $1 of the stock price. If the underlying stock moves again to $153.50, the new option price in this case will be $2.00.