Gamma
Description
The gamma measure describes how the delta of the option changes when the underlying asset changes. Hence, the gamma also describes how the you should change your hedge to remain delta neutral when the spot moves. All purchased standard options, calls and puts, have positive gamma.
The gamma position also provides insight into the investor's view on the volatility of the underlying asset, as a long position shows expectations of a volatile market while a short position indicates that he/she expects a calm market (see Gamma scalping vs. bleeding for more information).
Technical Description
The second derivative of the option price with respect to the underlying asset (the convexity of the option's price-curve at the spot rate).

