Madame Giry is an aging woman who works as a concierge in the rue de Provence, who looks after patrons of the Opera, principally those who sit in the boxes.
Once the managers have returned to their office, the Ghost steals the money from this pocket with the help of a trapdoor built into the floor.
During a meeting with the managers, she explains that she once found a note in Box Five, written by the Ghost and listing a number of dancers and singers who married into royalty and the nobility, with her daughter Meg included as eventually becoming an empress.
This note was enough to persuade Madame Giry to help the Ghost; later in life, Meg did become the Baroness de Castelot-Barbezac.
In Andrew Lloyd Webber's The Phantom of the Opera, Madame Giry's role is changed to become a slightly younger woman who now works as a choreographer of the corps de ballet.
When the Opera Diva, Carlotta Giudicelli, walks out during rehearsals at the start of the show, it is Madame Giry, and her daughter, Meg, who suggest Christine Daaé for the leading role.
In the 2004 film version of the musical (in which she is played by Miranda Richardson), Madame Giry is shown almost to be an accomplice of the Phantom, failing to notify people when he locks Christine's dressing room (though she could have alerted someone, but they likely did not listen) or when she spots him in the rafters during a scene.