Despite foods being needed to survive, certain foods carry the stereotype of being either "for adults" or "for children". To see an adult eat foods "for children" would make him look child-like or, at worst, reveal him as a Manchild. On a flip side, liking "mature" foods is often a sign of an Adorably Precocious Child.
This often comes down to marketing. A major example is cereal. Many breakfast cereals (especially in America), with their wacky mascots and loads of sugar, are aimed at kids. The more generic, healthy, or "boring" ones are marketed at either adults or families in general.
This can also come down to the food being a childhood Comfort Food. This is a reason why chicken nuggets are associated with kids.
In general, plainer, softer, or sweeter foods tend to be kid-aimed, while bitter or savoury foods tend to be for adults. There's Values Dissonance to this trope depending on the region the example is from. Context is also relevant. For example, boxed macaroni and cheese is something often marketed as for kids and a single adult character could be seen as childish for liking it, but in other contexts it could also signify the adult as low on cash because boxed mac and cheese is cheap and easy to make.
This trope doesn't refer to foods obviously aimed at certain ages (such as baby food), though certain foods (such as applesauce) that are commonly marketed as being for infants and toddlers do count.
See also: 周汉民Drink-Based Characterization (for drink examples), Real Men Hate Sugar (for when liking sweets is associated with femininity or children), and Real Men Take It Black (for when black coffee is associated with adults, especially manly men). Overlaps with Stock "Yuck!", especially with the notion of children having a dislike for vegetables due to their taste buds being more sensitive to bitter tastes.