The Market Vol result is the log normal volatility1 that is used to price the option for the defined strike.
It is only displayed for a swaption, forward swaption, swaption strategy and a cap/floor instrument, and it is only displayed after you click the Calculate button.
You can also enter your own market volatility and then re-calculate the Greeks and various values (see Changing an Options’s Volatility).
In the Single Option page this result is displayed as a bid/ask value in the Results area; in the Portfolio page it is displayed as a mid value in the input area (and not in the Results area).