Option’s speed measures the change in gamma with respect to the change in price of the underlying asset, all other things being equal. Mathematically, a dGamma/dSpot is the 1st derivative of the gamma of the price of the underlying asset or a 3rd order derivative of the price of an option with respect to the price of the underlying asset.
Traders use a gamma to determine how much to hedge a position when the price of an underlying asset moves. For example, if a share changes by $1, the delta will change by the amount of the gamma. But this is only an approximate change in the delta. Therefore, higher order derivatives are required for a more accurate delta change.
Gamma is very important when there is less than one week left before an option expires, because the gamma tends to grow for at the money options as the option approaches expiry date. Vega, on the contrary, decreases as the time passes (for OTM, ITM and ATM options).