Gamma is the change in delta per $1 move in the stock, the curvature of the position. It peaks at the money and grows sharply as expiration approaches. Long option positions own gamma; short positions owe it.
Gamma is why near-dated short options are dangerous out of proportion to their premium: a strike that was comfortably out of the money at 10 DTE can become an at-the-money coin flip on one ordinary move, with delta snapping from small to large. The 30-45 DTE entry convention and the 21-DTE exit convention in premium-selling disciplines are, at bottom, gamma management. At the market level, aggregate dealer gamma positioning is estimated as GEX.