The film begins with Mary Poppins (Julie Andrews) perched on a cloud high above London in Spring 1910. The action descends to earth where Bert (Dick Van Dyke), a Cockney jack-of-all-trades is performing as a one-man band at a park entrance. After the show, he breaks the "Fourth wall" and introduces the audience to the well-to-do but troubled Banks family, headed by the cold and aloof Mr. Banks (David Tomlinson) and the loving but highly distracted suffragette Mrs. Banks (Glynis Johns).
The Banks' latest nanny, Katie Nanna, quits out of exasperation after the Banks children, Jane (Karen Dotrice) and Michael (Matthew Garber) run off in pursuit of a wayward kite. Mr Banks returns home from his job at a bank, and Mrs Banks reveals the children are missing. A policeman arrives with the children, who ask their father to help repair their damaged kite, but he dismisses them and advertises for an authoritarian nanny-replacement. Jane and Michael draft their own advertisement asking for a fun, kind-hearted and caring person, but Mr. Banks tears up the paper and throws it in the fireplace. Unnoticed, the note's remains float up the chimney.
The next day there is a queue of old and disagreeable nanny candidates waiting at the door. However, a strong gust of wind literally blows the queue away, and Mary Poppins floats down with her umbrella to apply. Mr. Banks is stunned to see that this calmly defiant new nanny has responded to the children's ad despite the fact he destroyed it. As he puzzles, Mary Poppins employs herself and begins work.
The children face surprises of their own: Mary possesses a bottomless carpetbag, and makes contents of the children's nursery come to life and tidy themselves. The trio then meet Bert in the park, where Mary uses one of his chalk pavement-drawings as a gateway to an outing in an animated countryside. The next day, they all visit Mary's jovial Uncle Albert, who floats whenever he laughs, and join him in a tea party in midair.
Mr. Banks grows uncomfortable with his children's stories of their adventures, but Mary effortlessly inverts his attempted dismissal of her services into a plan to take his children with him to the bank where he is employed. Mr. Dawes, Mr. Banks' extremely elderly employer, aggressively tries to persuade Michael to invest his money in the bank. When Michael protests, the other customers misunderstand, and start a run on the bank that forces the bank to suspend business. The children flee and wander into the slums of the East End of London. Fortunately, they run into Bert, now employed as a chimney sweep. He takes them safely home, explaining that their father does not hate them, but that he has problems of his own, and that unlike the children, has no-one to turn to but himself.
At home, a departing Mrs. Banks employs Bert to clean the family's chimney and mind the children. Mary Poppins arrives back from her day off and warns of the dangers of this activity, but is too late as the children are both sucked up the chimney to the roof. Bert and Mary follow them and lead a tour of the rooftops of London that concludes with a joyful dance with Bert's chimney-sweep colleagues. A volley of fireworks from the Banks' eccentric neighbour, Admiral Boom, who thought London was being attacked by Hottentots, sends the entire gathering back down the Banks' chimney. Mr. Banks arrives home, forcing Mary to conclude the festivities. Banks then receives a phone call from work ordering him to return immediately for disciplinary action. As Mr. Banks gathers his strength, Bert points out that while Mr. Banks does need to make a living, his offspring's childhood will come and go in a blink of an eye, and he needs to be there for them while he can. The Banks children approach their father to apologise, and Michael gives Mr. Banks his tuppence in the hope that it will make things all right. Banks gently accepts the offering.
A sombre and thoughtful Mr. Banks walks alone through the night-time streets. At the bank, he is formally humiliated and sacked for causing the first run on the bank since 1773. However, after being at a loss when ordered to give a statement, Mr. Banks invokes Mary Poppins' all-purpose word "Supercalifragilisticexpialidocious!" to tweak Mr Dawes. He gives Dawes the tuppence, tells the old man one of Uncle Albert's jokes and raucously departs. Dawes mulls over the joke, finally "gets it" and floats up into the air, laughing...
The next morning, the winds have changed direction, and so Mary must depart. Meanwhile, the Banks adults cannot find Mr. Banks, and fear that he might have become suicidal. However, Mr. Banks, now loving and joyful, reappears with the now-mended kite and cheerfully summons his children. The greatly-relieved Mrs. Banks supplies a tail for the kite, using one of her suffragette ribbons. They all leave the house without a backward glance as Mary Poppins watches from a window. In the park with other kite-flyers, Mr. Banks meets Mr. Dawes Jr., who says that his father literally died laughing. Instead of being mournful, the son is delighted his father died happy, and re-employs Mr. Banks to fill the opening as partner.
Her work done, Mary Poppins takes to the air with a fond farewell from Bert.
In casa Banks regna grande confusione perché la governante dei due fratellini molto vivaci si è licenziata. Il padre, non molto ottimista sulle possibilità di successo dei tentativi della sua "ingenua" moglie, si assume il peso di trovare una soluzione al problema e fa pubblicare un annuncio sul "Times". I due fratellini intanto preparano una canzone sulla quale scrivono come desiderano la governante. Di giorno puntualmente alle ore 8 una lunga fila di nuove "tate" attende di venir esaminata dal signor Banks. Richiamata da una bizzarra petizione dei due piccoli scende dal cielo una ragazza, la quale si presenta al padre e, dopo averlo sottoposto a delle domande, senz'attendere di essere a sua volta interrogata, gli comunica che metterà alla prova tutta la famiglia per una settimana, dopo di che deciderà se accettare o no il posto. Durante il periodo di prova, con grande gioia dei due bambini, capitano ai Banks ogni sorta di disavventure: il signor Banks viene persino licenziato. E ben presto la famiglia (soprattutto il Sig. Banks) impara quale sia il giusto tono della quiete e della serenità: tutto si sistemerà nel migliore dei modi e Mary Poppins torna da dove è venuta.