Okay...steeping. Obviously I'm a chef, not a chemist, and while molecular gastronomy is fun, it's not really my thing either. So, I'm not even going to attempt to tell you what's happening from a chemical perspective, and I'm not really certain anything actually is. Try to think of it as an infusion. If you put sliced pineapple into a jug of vodka and drank it straight off, it would taste like vodka and nothing else. But, if you let the pineapples sit in the vodka for a couple weeks or more, and then removed them from the jug, you would have pineapple infused vodka. I'm not sure this an entirely accurate description for what's taking place inside the bottle, but it's a good way to understand what happening inside the bottle.
A lot of people compare it to wine aging, as I've done in the past, but Varrius is partially correct in shooting that down. Wine aging occurs differently and does involve a chemical reaction, while it's not due to air being let in via the cork as stated (the cork is actually airtight creating a reductive atmosphere inside the bottle), it's a chemical reaction nevertheless.
I don't know if anyone knows for sure what's happening inside the bottle from a chemical perspective, but again, I suspect very little, if anything. As a community we simply don't have the resources to study how steeping occurs...we can barely find the resources to study the vapor itself. The best way to understand it is that it's the blended flavors coming together, as their viscosity may differ, and fully melding with the PG and VG which, also of differing viscosity, act as delivery agents for those flavor components.
I age with the lid on in a drawer in my house. Tobaccos get 2 weeks, bare minimum, being shaken every 1-2 days. I may taste throughout the process, I may not, but either way, if it's tobacco based, it's a 2 week minimum and often longer before I'll write a review on it. Fruit, candy, and bakery rarely require much steeping. If you're a DIYer, you'd want to give them a couple days, but if you're buying from a vendor, usually the shipping time is an acceptable period. That being said, most juice will improve, even if just a little, with age. So, if you have a juice you don't care for, put in a drawer for a couple weeks shaking it every 1-2 days, and see what you have at the end. Maybe it's the same, maybe it isn't....every juice is different.
Some people steep lid off, like Gthompson, I think that may lead to evaporation, thus changing the flavor and even possibly a breakdown of the nicotine, but again I don't know. Other people put it in a bowl of warm water for 15 min (that's called speed steeping), I've never done that so I can't comment on efficacy. I do it the old fashioned way because these juices are being reviewed and I want to give every bottle a fair shake.
That should cover it, but if anyone has more questions, fire away.