George Banks, an old-fashioned London banker, is trying to find a nanny for his two naughty children, Jane and Michael, as several nannies have now upped and left. His children produce an advertisement for their ideal nanny ("with a cheery disposition, rosy cheeks, play games - all sorts", etc). George tears it up and throws it away.
Floating down from the sky, the "practically perfect" Mary Poppins arrives, having rescued the remains of the children's advertisement. She charms George into giving her the job, and soon delights the children with her songs and magic, while remaining extremely firm and militant, and only promising to stay until the wind changes.
She takes them on several outings, including jumping through a chalk picture into the countryside, accompanied by Bert, an odd-job man with an (appallingly imitated) cockney accent. They also visit uncle Albert, a man who can't stop laughing, and have a tea party on the ceiling.
George is infuriated that the children are doing such frivolous things, and tries to sack Mary Poppins, but she suggests he takes the children to his bank. Michael has taken tuppence "to feed the birds", but an eccentric elderly man at the bank steals it. The children run away, and bump into Bert, who is now a chimney sweep.
He takes the children, and Mary Poppins, up the chimney and on to the roof, where they dance, along with many other chimney sweeps.
Meanwhile, George has lost his job at the bank. However, he is suddenly much more cheerful and fun loving.