What does it mean to wait in the west wing of the moon?

The Poems Written by Cui Yingying to Zhang Sheng in The West Chamber;

Under the west wing of the moon, the windward door was half open.

The flowers on the wall are moving, and it is suspected that they are jade people.

Let her maid, the matchmaker, give it to Zhang Sheng. The matchmaker is not very literate and doesn't understand the meaning, but Zhang Sheng understood at a glance: this is the lady who asked him to come over at midnight and open the door for him.

In the middle of the night, Zhang climbed over the wall and left. Unfortunately, however, my mother was in the room, and the young lady had to secretly ask the matchmaker to pick up Zhang. The clever matchmaker hid Zhang and fooled his wife. After his wife left, Zhang He was able to meet.