Sherwood Forest was a wooded area in England. The region was associated with Nottingham and Nottingham Castle in the tales of Robin Hood, a mythological leader of a band of outlaws in 12th century England. In the tales, this forest was the abode of Robin Hood and his Merry Men.
In 2367, Q sent Starfleet Captain Jean-Luc Picard and the command crew of the USS Enterprise-D into a recreation of the 12th century setting in order to prove that Picard had feelings for Vash.
To that end, Q turned Vash into Maid Marian, Picard into Robin Hood, and the rest of the command crew into the other famous characters. Picard had to rescue Vash from Nottingham Castle as she had agreed to marry Sir Guy of Gisbourne in order to avoid being executed. (TNG: "Qpid")
In 2369, Miles O'Brien recalled these events when he mentioned to the senior staff of Deep Space 9 that Vash and Q had "met in Sherwood Forest". (DS9: "Q-Less")
The scenes in Sherwood Forest were filmed on Tuesday 12 February 1991 on a location shooting at Descanso Gardens. Several close-ups with the actors were later filmed outside Paramount Stage 16.