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.:
where P is the price of the derivative
and S is the price of the underlying
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.