Here is some narrative explanation from D&D's past, page 40 of the 1e DMG by Gygax:
SPELL CASTING
All magic and cleric spells are similar in that the word sounds, when combined into whatever patterns are applicable, are charged with energy from the Positive or Negative Material Plane. When uttered, these sounds cause the release of this energy, which in turn triggers a set reaction. The release of the energy contained in these words is what causes the spell to be forgotten or the writing to disappear from the surface upon which it is written.
The triggering action draws power from some plane of the multiverse. Whether the spell is an abjuration, conjuration, alteration, enchantment, or whatever, there is a flow of energy — first from the spell caster, then from some plane to the area magicked or enspelled by the caster. The energy flow is not from the caster per se, it is from the utterance of the sounds, each of which is charged with energy which is loosed when the proper formula and/or ritual is completed with their utterance. This power then taps the desired plane (whether or not the spell user has any idea of what or where it is) to cause the spell to function. It is much like plugging in a heater; the electrical outlet does not hold all of the electrical energy to cause the heater to function, but the wires leading from it, ultimately to the power station, bring the electricity to the desired location.
Many spells also require somatic motions in conjunction with words. The spoken words trigger the release of the magical energy, and the hand movements are usually required in order to control and specify the direction, target, area, etc., of the spell effects. When spell energy is released, it usually flows to the Prime Material from the Positive or Negative Material Plane. To replace it, something must flow back in reverse. The dissolution and destruction of material components provides the energy that balances out this flow, through the principle of similarity. Sometimes this destruction is very slow, as is the case with druids’ mistletoe. Those spells without apparent material components are actually utilizing the air exhaled by the magic-user in the utterance of the spell.
Release of word/sound-stored energy is not particularly debilitating to the spell caster, as he or she has gathered this energy over a course of time prior to the loosing of the power. It comes from outside the spell caster, not from his or her own vital essence. The power to activate even a first level spell would leave a spell caster weak and shaking if it were drawn from his or her personal energy, and a third level spell would most certainly totally drain the caster’s body of life!
Because spells tap power from other planes, any improper casting is likely to cause the spell not to function (the heater is turned on, but you haven’t plugged it in, or you’ve plugged it in but not turned it on) or to malfunction (you held onto the prongs of the plug when you tapped the current, or you accidently dropped the heater as you were plugging it in, or perhaps you plugged in some other appliance or device by mistake). Such happenings are covered in the various chances for spell malfunction. If your players inquire as to how spells work, or fail to do so, you can explain, without difficulty, the precepts of the AD&D magic spell systems. (For background reading you can direct campaign participants to Vance’s THE EYES OF THE OVERWORLD and THE DYING EARTH as well as to Bellairs’ THE FACE IN THE FROST.)
