In Edwardian London, 1910, Bert entertains a crowd as a one-man band when he senses a change in the wind. Afterwards, he directly addresses the audience, and gives them a tour of Cherry Tree Lane, stopping outside the Banks family's home. George Banks returns home to learn from his wife, Winifred, that Katie Nanna has left their service after Jane and Michael ran away again. They are returned shortly after by Constable Jones, who reveals the children were chasing a lost kite. The children ask their father to help build a better kite, but he dismisses them. Taking it upon himself to hire a new nanny, Mr. Banks advertises for a stern, no-nonsense nanny. Instead, Jane and Michael present their own advertisement for a kinder, sweeter nanny. Mr. Banks rips up the letter, and throws the scraps in the fireplace, but the remains of the advertisement magically float up, and out into the air.
The next day, a number of elderly, sour-faced nannies wait outside the Banks' home, but a strong gust of wind blows them away, and Jane and Michael witness a young nanny descending from the sky using her umbrella. Presenting herself to Mr. Banks, Mary Poppins calmly produces the children's restored advertisement, and agrees with its requests, but promises the astonished banker she will be firm with his children. As Mr. Banks puzzles over the advertisement's return, Mary Poppins hires herself, and convinces him it was originally his idea. She meets the children, then helps them tidy their nursery through song, before heading out for a walk in the park.
Outside, they meet Bert, working as a screever; Mary Poppins uses her magic to transport the group into one of his drawings. While the children ride on a carousel, Mary Poppins and Bert go on a leisurely stroll. Mary Poppins later enchants the carousel horses, and participates in a horse race, which she wins. While being asked to describe her victory, Mary Poppins announces the nonsense word "Supercalifragilisticexpialidocious". However, the outing is ruined when a thunderstorm dissolves Bert's drawings, returning the group to London.
On another outing, the four meet Uncle Albert, who has floated up in the air due to his uncontrollable laughter; they join him for a tea party on the ceiling, telling jokes.
Mr. Banks becomes annoyed by the household's cheery atmosphere, and threatens to fire Mary Poppins. Instead, Mary Poppins inverts his attempt by convincing him to take the children to the bank for a day. Mr. Banks takes Jane and Michael to the bank, where they meet Mr. Dawes Sr, and his son. Mr. Dawes aggressively attempts to have Michael invest his tuppence in the bank, snatching it from him. Michael demands it back, causing other customers to misinterpret, and all demand their own money back, causing a bank run.
Jane and Michael flee the bank, getting lost in the East End until they run into Bert, now working as a chimney sweep, who escorts them home. The three and Mary Poppins venture onto the rooftops, where they have a song-and-dance number with other chimney sweeps, which spills out into the Banks' home. Mr. Banks returns, and receives a phone call from his employers. He speaks with Bert, who tells him he should spend more time with his children before they grow up. Jane and Michael give their father Michael's tuppence in the hope to make amends.
Mr. Banks walks through London to the bank, where he is given a humiliating cashiering, and is dismissed. Looking to the tuppence for words, he blurts out "Supercalifragilisticexpialidocious!", tells one of Uncle Albert's jokes, and happily heads home. Dawes mulls over the joke, but finally "gets" it, and floats up into the air, laughing.
The next day, the wind changes, meaning Mary Poppins must leave. A happier Mr. Banks is found at home, having fixed his children's kite, and takes the family out to fly it. In the park, the Bankses meet Mr. Dawes Jr, who reveals his father died laughing from the joke, and re-employs Mr. Banks as a junior partner. With her work done, Mary Poppins flies away, with Bert bidding her farewell, telling her not to stay away too long.