Dick Van Dyke and Julie Andrews (top) and Karen Dotrice and Matthew Garber (bottom) in a scene from Mary Poppins. The Kobal Collection. Reproduced by permission.

Mary Poppins is a magical governess who, in her original incarnation, has an incalculable effect on the four Banks children—Jane, Michael, and twins John and Barbara—in early twentieth-century London. She started out as the central character in a series of books penned by Australian-born writer P. L. (Pamela Lyndon) Travers (1899–1996). The first was titled Mary Poppins (1934). Travers's Mary may be strict and egotistical, but she is no ordinary nanny. Among her talents are sliding up banisters and communicating with animals—and herein lies her charm.

Travers's character gained her most everlasting popularity in a delightful feature film, co-produced by Walt Disney (1901–1966) and released by his studio. The film deftly blends music and comedy, live action and animation. This...