One of the first adventures on which Mary takes the kids is inside a chalk drawing. Bert draws a bunch of different pictures on the sidewalk—one of the English countryside. They jump into it, and find themselves in a completely animated world. They sing with talking animals, save a fox from a foxhunt, and Mary winds a horse race. Also, Bert dances with a bunch of penguins who dress as waiters.
This animated sequence manages to kill a lot of time in the movie with pure entertainment—it's mostly musical, with songs like "It's a Jolly Holiday" and "Supercalifragilisticexpialidocious." It's not super-focused on story, but more on amusing the audience. (Not everything has to be strictly plotted).
But the sequence also says something about the power of the imagination. Even if you can't literally jump inside a chalk drawing, you can voyage into other worlds through the kind of art and creativity Bert used to make those drawings.
When they return to the real world—after the rain washes away the chalk drawings—Mary denies that they ever ventured inside a chalk-drawing world. Michael reminds her that she won a horse race:
MARY: A respectable person like me in a horse race? How dare you suggest such a thing.
MICHAEL: But I saw you do it!
Regardless of whether Michael really saw it—or whether it was pure fantasy—it symbolizes the same point. Imagination can take us into new worlds, be it Narnia, Middle Earth, or Mary Poppins' version of London.
Yeah, that's a pretty saccharine statement to say to anyone older than ten. But since Mary Poppins was aimed at the juice-box set, we think its pretty charming.