Definition
Gamma is the second derivative of option value with respect to the underlying - the rate at which delta changes.
What being long gamma feels like
You own a call, delta 0.5, and you are hedged short 0.5 shares. You are delta-neutral, so small moves do nothing at first order.
But if the stock rises, your delta rises above 0.5 - you become net long into a rising market. If it falls, your delta falls below 0.5 - you become net short into a falling market.
You are automatically positioned in the direction the market moved. That is convexity, and it is why long gamma profits from movement regardless of direction.
The mirror image: short gamma means you become short as the market rises and long as it falls - positioned wrongly both ways.
What you pay for it
Nothing is free. The cost of long gamma is theta, the decay of the option's value over time.
The relationship is essentially: your gamma profit depends on realised volatility, and your theta cost depends on implied volatility. Own options and you profit if the market moves more than the price implied. See implied volatility.
That is the fundamental trade in options market making, and being able to state it cleanly is a strong interview signal.
Where gamma is largest
At the money, near expiry. An at-the-money option on expiry day has a delta that flips between 0 and 1 on tiny moves, which is enormous gamma.
That concentration is why expiry-day risk management is difficult, and why desks reduce at-the-money exposure into expiry.
Deep in- or out-of-the-money options have very little gamma - their delta is pinned near 1 or 0 and barely moves.
The interview question
"You are long gamma and delta hedged. The stock is very volatile but ends the day unchanged. Do you make money?"
Yes. Every hedge adjustment along the way buys low and sells high - see gamma scalping. The path is what pays you, not the endpoint.
Practise in finance and derivatives.