The nut flush is the best possible flush available. Typically it will be an ace high flush so long as a straight flush is not possible, but if the ace is on the board then the nut flush is held by the player whose flush includes the highest ranking suited card not on the board. If a running flush is possible, that would become the nuts (rather than an ace-high normal flush).
For example, if the board shows Ah Qh 7h 3c 10d then the nut flush would be made with the Kh and any other heart.
In hold’em three of a suit must be on the board for a flush to be possible. If a player holds 2 suited hole cards, and 2 cards of the same suit come on the flop they have a flush draw, also known as a 4 flush, needing only one further suited card to complete. If they hold the ace, or the highest suited card not on the board then they have the nut flush draw.
