Celia is Mr. Peachum's wife. She doesn't have too much of a dynamic role in the play. She seems to be there to set Peachum up for his stinging, mean attacks. She's like a sidekick, or a lapdog.
When Peachum wants to put Macheath in jail, Celia's the one who does his dirty work. She promises the prostitutes money if they'll betray Mac. When Polly visits Mac in prison, Celia's the one who drags her back home.
While she doesn't have much oomph on her own, Mrs. Peachum works like a foundation for the other characters. She represents society's rules and, even if she doesn't care too much about the spirit of the law, she's there to make sure the letter is enforced.