The book is about a young lad, Nils Holgersson, whose "chief delight was to eat and sleep, and after that he liked best to make mischief". He takes great delight in hurting the animals in his family farm. Nils captures a tomte in a net while his family is at church and have left him home to memorize chapters from the Bible. The tomte proposes to Nils that if Nils frees him, the tomte will give him a huge gold coin. Nils rejects the offer and the tomte turns Nils into a tomte, which leaves him shrunken and able to talk with animals, who are thrilled to see the boy reduced to their size and are angry and hungry for revenge. While this is happening, wild geese are flying over the farm on one of their migrations, and a white farm goose attempts to join the wild ones. In an attempt to salvage something before his family returns, Nils holds on to the bird's neck as it successfully takes off and joins the wild birds.
The wild geese, who are not pleased at all to be joined by a boy and a domestic goose, eventually take him on an adventurous trip across all the historical provinces of Sweden observing in passing their natural characteristics and economic resources. At the same time the characters and situations he encounters make him a man: the domestic goose needs to prove his ability to fly like the experienced wild geese, and Nils needs to prove to the geese that he would be a useful companion, despite their initial misgivings. During the trip, Nils learns that if he proves he has changed for the better, the tomte might be disposed to change him back to his normal size.
The book also includes various subplots, concerning people whose lives are touched in one way or another by Nils and the wild geese. For example, one chapter centers on a young provincial man who feels lonely and alienated in the capital Stockholm, is befriended by a nice old gentleman who tells him (and the reader) about the city's history - and only later finds that it was none other than the King of Sweden, walking incognito in the park.
The book was criticized for the fact that the goose and boy don't make any stop in the province Halland. In chapter 53 they fly over Halland on the way back to Scania, but they aren't impressed by the sight and they don't stop. However, such a chapter has been added to some translations of the book. In depictions Nils is usually wearing a red cap, although this is erroneous as he is described in the original Swedish edition as wearing a white cap.

Question: What does Nil have to prove to the wild geese?
Answer: he will be a useful companion
Alternative answer: That he would be a useful companion.