Delta is how much the option price will change relative to the stock price changes, and gamma is how much the delta will change as the stock price changes.

Imagine a stock is $100 per share. You buy a call option for $1.00 with a delta of 0.10. If the stock goes to $101, your option is worth $1.10.

At the same time, as the underlying price changes, the delta itself will change. So imagining the above option has a gamma of 0.01. After the underlying moves to $101, the option delta is now 0.11. So if the price moves up again to $102, the option is now worth $1.21 and the new delta would be 0.12.