Magical ability or magic is defined as the capacity an intelligence has to transform the mind's ideas into real energy; expressed as change in reality.
There is a principle which states that energy can never be created nor destroyed. Magic seems to break this rule, but it doesn't. This may seem obvious when, for example, a magician invokes a burning ball of fire between his hands. The world, which is dualistic, also contains another kind of non-physical energy which I'll refer to as aether. Remember that energy is purely physical.
As such, when a sorcerer casts a spell he's not creating energy, he's obtaining physical energy from non-physical energy or aether. He's transforming aether into energy. This is done through intelligence, through consciousness. Aether isn't generated either. The universe contains a fixed amount of total energy, which is the sum of physical energy and aether. Aether can turn into energy through magic and energy can turn into aether through some natural processes and (reverse) magic as well. There is equilibrium.
Not all aether is transformable. There is non-magical aether which can't be used to generate energy. There are several types of aether, which will correspond to the different schools of magic (types of magic). The relationship between aether and energy is not well understood, but it's known through experience: there is a kind of aether, for example, which corresponds to water. Even though matter has only quantitative difference (gold is different from iron only by the number of protons), the different types of aether seem to be qualitative. If they're quantitative, the underlying structures are not understood.
Aethers can have counterparts. For example, the counterpart of igneous aether (fire) is aqueous aether (water/ice); this is the reason that fire magic opposes water magic, even though, physically, water and fire wouldn't disappear if meeting. Magically-generated fire and magically-generated water would.
But before that, it's important to talk about the different states of aether and the cyclic nature of reality.
Aether-Energy balance or cycle.
Normal aether permeates space and doesn't have a physical representation. It's called inert aether. Some magical beings are purely made of inert aether and have no body; they can feed on physical energy by turning it into inert aether by something we should call "inverse magic". The effect is like if energy was unexplainably dragged from our universe.
Inert aether is attractive to itself. Pure aether can be called "arcane aether". It's also attracted by intelligent minds, but the attraction to itself is much bigger. It tends to naturally form rivers and lakes of aether, but different types of aether meeting can provoke all kind of reactions and cycles. For example, the two aethers described above (igneous and aqueous), if meeting, would behave something like an electron and a positron: they annihilate, liberating "energy" (and exploding). But since aether is already "energy", what they liberate is just a different type of aether. It's all very complex, but the result is a world with a capricious but stable distribution of aether, the "rivers" are called ley lines and it's rare to find a "dry area".
When inert aether is close to an intelligent being, it's attracted. Intelligent beings store different amounts of energy in their souls. Normally, it's full, so if you're close to a ley line all the aethers won't stop their flux to follow you (and if you weren't, they probably wouldn't either since they're moving due to more powerful forces). When aether enters the soul, it turns into static aether. The content of static aether measures the amount of energy that can be produced by the being through magic. It's a special aether, since it has a physical correspondence called mana. Mana is commonly called magical energy and is the amount of physical energy a being has to produce magic. The maximum depends on the species and training. This maximum quantity is called the mana pool, and you measure mana in mana points which correspond to joules, since it's a form of energy. It's consciousness which makes the aether have a physical expression.
The mana pool has a limit because a given intelligence has a limit as to the energy it can contain. If it gets saturated, it will stop controling some of it which will become inert aether, vanishing from the physical world.
Static aether can be converted by the intelligence into dynamic aether. Dynamic aether is dualistic: it has an underlying reality in the non-physical world, but it has a direct physical effect, dependent on the non-physical one. It's the real magic. It's the effect a spell has: it provokes motion, heat, transformations, creates matter... to sum up, the aether creates a shade of physical energy. As long as this is controlled by the caster, it will maintain a dualistic nature. When that ceases, if the physical part is still present, the energy will simply turn into (well, it is) normal energy and the aether part will completely disappear, since its representation now has gained the real existence.
After this, the cycle can begin again by a non-physical entity dragging energy from the world to transform it to non-physical aether. There is an equilibrium.
Let's see a simple practical example: two sorcerers casting two wind spells in the same direction. Let's say the motion the spell provokes in the air needs you to waste 5 J of energy. Well, at some point, aereous aether (wind aether, for short) has entered the sorcerers' bodies. Aether is measured in aetherials ("ae" is the unit symbol; "ar ae" for wind). This inert wind aether turned into static wind aether upon entering their souls. Since they are casting a wind spell, they know they need to have wind aether in their mana pools. Intelligence can generally change at will one type of aether into another one, so it doesn't matter which kind you have stored, it's all "unmarked". They cast the spell, turning 5 ar ae into dynamic wind aether and their shade: 5J of real energy in the motion of the wind. They add up creating a breeze equivalent to 10 J of motion, because there are 10 ar ae in the non-physical world operating that way. Once they finish the spell, at a given time, this energy still lingers the real world, but the 10 ar ae have disappeared. This shows that, while casting a spell, the physical vs. non-physical distinction is blurred, which is why magic operates distinctly from physical events. After the spell, there are 10 J more of energy in the total net energy of the universe, but 10 ae less, creating a balance.
As such, there are three types of events in the universe: purely physical events (no change in aether), magical events (changes in both planes), and purely non-physical events (which only comprise changes in aether, but not energy).
By the way, one aetherial (1 ae) is defined as the non-physical energy needed for an intelligence to cast a spell which expresses an energy of 1 J (joules are the units of physical energy in our world).
Next time I'll post a bit about the different schools of magic and more about magic generation (spellcasting).
I hope you find this interesting, sorry if this post was too long. I'll be glad to clarify or respond to any question.