Magical energy follows a continuum, but it is generally divided into two main kinds by function:
Od, the colourless energy, provides form. It is a passive energy existing in all the universe, and when concentrated it becomes physical matter.
Seidr, the coloured energy, provides shape. It is an active energy produced by thought and movement, and when concentrated it becomes spirits and concepts.
To cast a spell the caster must provide both seidr and od, the first binding the second in a sort of lattice. While typically the seidr is provided by the caster himself, the source of od varies. Releasing and shaping seidr in the correct manner normally requires a careful series of movements - doing so from thought alone requires great willpower and skill. This structure is fragile however - breaking it frees the od and ends the spell. Fighting styles have been developed which take advantage of the seidr produced by a fighter's movements to disrupt the seidr involved in casting.
Clerics and similar casters receive od from their deity, in exchange for the seidr provided by worship. As such it is "tinted", closer to seidr than normal. Since it already has some structure it is easier to provide more (requiring less movement), but likewise harder or impossible to use it for tasks which do not fit the nature of the energy.
Certain creatures have such enormous supplies of od that they can release it in raw form, most famously dragons with their breath weapons. Spellfire is another example of this ability.
Psionic powers differ from spells, being a homogenous mass of near-od rather than a blend of multiple energies. To achieve the deisred effect, a psion focuses on a related concept or ideal so intently that the od of his body becomes coloured by it, then expels raw energy in a similar manner to the creatures above. Techniques which affect his body alone use only the first step.
Typically, concentrated od makes up a creature's physical body while seidr makes up its soul. However, some creatures have "veins" of seidr present in their physical bodies (whether by chance or purposefully inscribed). They may use these as a template in casting instead of learning to sculpt their own, resulting in magic coming easily to them. These are creatures with sorcerer casting or spell-like abilities, depending on whether the veins are wide or deep respectively. Usually these veins are hard to detect, but some families in Eberron display them visibly.
Antimagic fields consist of a net of seidr which binds to any od in the area and renders it inert. The od within a spell can be shielded from this effect if its seidr is sufficiently dense. (eg. epic spells) Force spells are resistant to antimagic due to containing a larger ratio of seidr to od, with the od entirely covered by the seidr.
One of the first things taught to any conventional wizard in the process of taming the power is the eight schools of magic, also known as the Eight Brothers. Representing magic as a group of people helps the caster visualise their power, and pick out the effect they want from the endless possibilities. Other traditions of magic use different representations, and thus the borders between different types of magical study do not line up between, for instance, a wizard and a wu jen.
One influential wizard's school decided at some point in the past to teach cure wounds as part of the conjuration school, for political reasons; casters from distant regions still cast it as a necromancy spell.