It is mostly a fancy way of saying that they are combining flavors. There are no solid, physical layers involved anywhere.
Still, there is a reason why the "layering" metaphor is more apt than simply saying "combining". Flavor is mostly about aroma, which leads to two aspects of "layering".
First, aroma is not perceived all at once when you bite off. You first notice the most volatile smell notes when the food enters your mouth, go through a kind of "middle" and only at the end, while swallowing, you notice the "heavier" flavor. So, when seasoning, you can work with food such that you don't mix up too many flavors in one of the three aroma "layers", but also to make sure that there is something noticeable in each of the three.
Second, people are accustomed to some flavors being present as a metaphorical "background" taste. It can happen that, if the expected aroma is absent, you can add all the spices you want, and the eater will still experience it as underseasoned. This is what is happening in the example you cited: the "base layer" are the onion and garlic, which are probably the standard for the dish, and then you can take that dish in different directions by your choice of additional herbs and spices. In that case, you can see the metaphor as akin to clothing - once you have a basic shirt on, you can always make the outfit nicer by layering a scarf, jacket or jewelry on top of it.
All in all, it is not "all about layering flavors". It is just an expression which helps some cooks go about creating harmonious flavor combinations. If it works for you, use it. If not, learn to think about your seasoning in other terms.