I know why the mage can cast a fireball spell once per day, he has the spell recipe for it, he forgets the recipe after casting, and needs a full rest to restore it. The mage may not understand why this works, he just know that it does. That's an external process, what the mage thinks about the process is irrelevant.
And have you ever stopped to think about how that magic actually does work? Even if it isn't something the wizard needs to think about, how magic works is a really critical question for any fantasy setting.
I have seen plenty of fantasy settings that go into a great deal of depth for how their magic systems work. For example, WotC's other big property, Magic: the Gathering, has a fairly well-detailed and explained magic system. Mana is the fundamental building block of reality and comes in five flavors. By drawing upon sources of mana found in the land, mages can shape that mana to cast spells.
For an example from a completely different genre, the Naruto manga/anime has a very detailed magic system. The source of all powers is chakra, the mix of mental and physical energy within the body. This chakra flows through a complex network within the body. Chakra can be used for three different kinds of powers: taijutsu (purely physical arts), genjutsu (mental illusions caused by sensory stimulus), and ninjutsu (magical conjuration and evocation). Furthermore, chakra comes in five "natures", based on elemental properties: fire, water, wind, earth, and lightning. Everyone has a natural disposition towards one of the five natures, and even the very best masters will usually only master two or three. By manipulating chakra and the natures through special techniques and hand-signs, it is possible to produce everything from super-human punches to teleportation and summoning arts.
That is a well-explained and robust magical system. It explains both the source of power the magic is coming from, and how a magic user uses it.
D&D doesn't do this. D&D magic works on the principle of: "don't think too hard about it." Since all supernatural powers in D&D already fall under the purview of "don't think too hard about it", why can't we apply that logic to martial stuff as well?