Idk. I used the term steep because it seems to be an accepted term for this process by the community, as opposed to its function. As far as the question of what really happens to the juice, no one really knows (yet). I have a hunch that it is about air exchange. There is no doubt that some substances (such as alcohol) have volatile fractions that will off-gas when the cap is left off the bottle. Other changes can happen to other substances when the air is exchanged in the bottle. The air in the mixing lab where the juice was made has different levels and types of "impurities" than the air in your home, and perhaps this is responsible for some of the changes. Other hypotheses include oxygenation and other gas exchanges (remember that air is only about 20% oxygen, the rest is nitrogen and other gases). Flavor components "spreading out" into the VG and/or PG base(s) in the bottle would occur whether the lid is on or off, so length of time in sitting is the factor there. Without an analysis lab equipped with a gas chromatograph olfactometer, an electrogustometer, and other fancy expensive machines to test juices in different stages, it is really hard to determine what is actually occurring. Anecdotal evidence suggests that, whether you want to call the process steeping, aging, breathing, what-have-you, cap-on/cap-off, shaking, letting it sit for ? hours/days/weeks, etc., improves the flavors of some juices. Why? How? Good questions.
Edit: side note, I received a card with my most recent arrival from Halo that said, "The taste of your Halo e-liquid will change considerably over the first 24-48 hours after being opened. When Halo e-liquid is kept too cold, the flavor can be diminished and even taste flavorless. As your e-liquid adjusts back to room temperature, the flavor will increase dramatically. Please do not refrigerate." This suggests to me that regardless of how long the juice sits after being made, it requires the act of opening to start the "steeping" process, lending to my theory about air exchange.