It's the area backstage where actors and dressers lurk during the show.

Why's it called a Green Room?

Many, many reasons have been suggested. Please don't bring this up
unless you have a definite cite for the origin of the phrase.

All that's agreed upon is:

The first known written use of the term is in 1701, and from the context
the writer (English owner-actor/playwright Colley Cibber 1671-1735, Poet
Laureate) expected people to recognise the term, so it was probably in
common use by the end of the 1690s.

Most lexicographers have concluded that the term did originate from the
colour the early greenrooms were painted, but no-one has any firm
reasons as to why they would have been painted green.

[Thanks to Spence Porter sporter@cat.nyu.edu]

There's also a suggestion it may be a corruption of 'scene room' or
'screen room' - a room where scenery was stored.

Some of the other (unsupported) reasons for the name that have been
suggested are:
   * Because the plays originally took place outside on the village
     green.
   * Because the artificial grass (green carpet) was stored there.
   * Because the green was soothing to actors eyes (after they had come
     off from performing in front of limelight)
   * Because limelight has a green tint to it, so it made sense to apply
     makeup in a room with a green tint
   * It was where the shrubbery used on stage was stored, and the plants
     made it a cool comfortable place
   * The 'green' was jargon for the section of the stage visible to the
     public, so clearly the 'green room' was the room nearest the stage.
     (I like this one, but I haven't seen a cite for it yet.)
   * The room was walled with green baize as soundproofing, so actors
     could practice their lines.