The gamma of a derivative (or portfolio) is the rate of change of its delta with the price of the underlying asset.
It is approximately the change in the delta that results from a one unit change in the price of the underlying.
More accurately (and more mathematically rigorously) it is the second derivative of the price of a derivative security against the price of the underlying security, i.e.:
Γ= (∂2P)/(∂S2)
where P is the price of the derivative
and S is the price of the underlying
The gamma of a derivative is used in constructing portfolios that are gamma hedged, which require less re-balancing than a purely delta hedged portfolio.
It can also be used as an indication of whether delta hedging is a sufficiently good strategy. If gamma is low, then delta hedging will be workable. If gamma is high the delta may be too sensitive to changes in the price of the underlying for delta hedging to be useable.