Let's say that you have a very young character, typically of an animal-like or otherwise non-human race, who has a very small physique overall. However, the character also has some bodily feature that seems to be disproportionately large compared to the rest of the body. That body part may be a tail, horns, a shell, or their hands/feet/paws. As the character is shown growing up, that bodily feature is shown to foreshadow how big the character will end up; in other words, the character will grow in such a way that said bodily feature will eventually no longer be disproportionately large.
The trope name comes from the idea that dog owners can predict how big their pets will get based on the size of their paws as puppies. In reality, this zigzags wildly based on the breed: while a mastiff puppy will likely have proportionally larger paws than a dachshund puppy of the same size, there are large dog breeds like collies that have small paws compared to the rest of their bodies both as puppies and adults. Purebreds are also more likely to follow this rule than mixed breeds.
- Hellboy's right arm, which looks only slightly larger than his left arm as an adult, was very large proportionally when he was little, to the point that as a baby it was about the size of the rest of his body. The reason it started off so disproportionate is because it technically wasn't his normal right arm: it originally belonged to a spirit who created the Ogdru Jahad before he was destroyed save for his right arm, which was eventually grafted onto the newborn Hellboy in the hopes that it could be used to reawaken the Ogdru Jahad.
- A Discussed Trope in the Vorkosigan Saga novel Komarr. Ekaterin holds up her hand next to her son's, checking to see if the tremor caused by his genetic disease is visible, and uses this to comment on how much he's growing.
"Hold out your hand. I want to see how much you have left to grow. Puppies with big paws are supposed to grow up to be big dogs, you know."
- Prince Sidon from The Legend of Zelda: Breath of the Wild is introduced as an uncommonly large Zora, specifically being twice as tall as the more averagely-sized Link. A flashback in "The Champions' Ballad" DLC shows that his head appendage was already longer than the rest of his body when he was a child even though he was half Link's height at the time.
- The human eyeball of all things is an exaggerated example. Not only will a person's eyeballs have reached almost full size by the age of three (and finished growing entirely by the age of 13), but all adults (regardless of gender or ethnicity) have the same sized eyeball, give or take a couple of mm. Hence why large eyes are associated with youth or cuteness and small eyes are associated with large individuals (technically making Puppy-Dog Eyes a manifestation of this trope).