A volatility surface is a graphical representation of the implied volatilities of options on the same underlying asset as a function of the option's strike price and expiration date. Volatility surfaces are often used in trading to identify opportunities for arbitrage and to make more informed decisions about the risk and potential returns of different options strategies.
There are several ways in which a volatility surface can be used in trading:

Identifying mispricings: A volatility surface can be used to identify discrepancies between the implied volatilities of different options on the same underlying asset or options with similar expiration dates but different strikes. If the implied volatilities of two options are significantly different, it may indicate an opportunity for arbitrage.

Determining the risk of different options strategies: A volatility surface can be used to assess the risk of different options strategies by comparing the implied volatilities of the options used in the strategy. For example, a trader could use a volatility surface to compare the implied volatilities of options with different strikes and expiration dates to determine which options are more or less risky.

Estimating the potential returns of different options strategies: A volatility surface can be used to estimate the potential returns of different options strategies by comparing the implied volatilities of the options used in the strategy. For example, a trader could use a volatility surface to compare the implied volatilities of options with different strikes and expiration dates to determine which options have the potential for higher or lower returns.

Assessing the impact of changes in implied volatility: A volatility surface can be used to assess the impact of changes in implied volatility on different options strategies. For example, a trader could use a volatility surface to compare the implied volatilities of options with different strikes and expiration dates to determine how changes in implied volatility might affect the value of the options.