The Market Normal Vol is the normal volatility1 that is used to price the instrument for the defined strike.
It is only displayed for a swaption, forward swaption and a swaption strategy, and a cap/floor instrument, and it is only displayed after you click the Calculate button.
For a swaption, forward swaption and swaption strategy you can also enter your own market normal volatility and then re-calculate the Greeks and various values (see Changing an Options’s Volatility). However, for a cap/floor this value is read-only.
In the Single Option page for a swaption, swaption strategy and forward swaption 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 in the MKT NVol field (and not in the Results area).