Long gamma means you get longer as the market rises and shorter as it falls - automatically positioned in the direction of the move. That is convexity, and it is why owning options profits from movement in either direction.
Short gamma inverts it: you are positioned wrongly both ways.
Highest at the money and near expiry, where a small move flips an option between in and out of the money.
What you pay for it: theta. Gamma profit tracks realised volatility; theta cost tracks implied.