Storybook homes are built in a whimsical and fairytale-esque style that was popular in the late 1910s to the 1920s. The style originated in the U.S., particularly in California. Although there is not much criteria defining this style, other than a general sense of playful whimsy, one of the textbook features is uneven/wonky roof lines, appearing undulating or even, and featuring gables, turrets, and dovecotes. Other common traits are cobblestones, wooden shutters, and mismatched windows and door.

The style mostly gained popularity in the U.S., probably due to the fact that the Old World aspects that it nods to were more novel and charming in the hills of California rather than in Europe where they could organically be found in older homes. One of the most famous storybook architects, Harry Oliver, who built the house pictured above, was also an Academy Award winning art director for films. This explains the kind of kitschy, Hollywood-style elements that define storybook homes. While it was mainly used for residential buildings, particularly gaining traction in the San Francisco Bay area which is notable for its eclectic architecture, there are some public buildings. The Charlie Chaplin studios, now known as the Jim Henson Company Lot, is built in the Storybook style (see below).

Vancouver has a famous Storybook home, known as the Hobbit House (officially, the James Residence). It was built in 1947, so earlier than the heydey of Storybook homes, but it undoubtedly owes itself to that architectural style. It is currently rented out. I have always found it very cute and charming, although I was dismayed to find that it looks quite stark and modern inside, and does not feature interior decor that matches the charm of the exterior.

Storybook homes are obviously quite eclectic, and I don’t know if everyone would want to live in one, but they are certainly fun to look at!
References
https://en.wikipedia.org/wiki/Storybook_house#Architects_and_examples