So what is temporal polyethism, and what is the advantage to honey bees?
Apis mellifera seems to be a species obsessed with efficiency and temporal polyethism is efficient. Why is temporal polyethism so efficient in worker honey bees?
Other social insect species and other social animal have division of labor. Some individuals may even perform multiple tasks in their lifetimes.
However, A. mellifera raises this to a whole new level by continuing to change physiologically as an adult, after full metamorphosis (egg, larva, pupa, adult stages) throughout its lifetime.
Those early developmental stages we call complete metamorphosis are enough for many insects, even social ones. A honey bee egg molting into larval form does need to be cared for by its older sisters until it has developed all the glands it will need in its lifetime, but emerges as a new “adult” from its pupal stage without wasting the hive’s energy resources for any development not essential at emergence.
For example, a newly emerged worker has no venom in its stinger sac. Guard duty is far in the future (maybe a whole couple weeks, possibly a 1/3 of its adult life) for this teenager. However, it's time to get to work right away cleaning while that bee's hypopharyngeal glands are developing. This teenager can perform tasks such as feeding older larvae with bee bread or nectar or honey mixed with pollen, until those glands are in full production. Once those hypopharyngeal glands are fully functional, the still developing adult bee can mix those gland secretions with others to make "royal" jelly. Now, this young adult transitions to feeding the youngest larvae as well as other adult bees, possibly including the queen.