Abjuration
Manipulation of Force
Abjuration magic is all about protection, warding, and countering. It has spells to negate both physical and magical onslaughts. A majority of abjuration spells carry a lawful essence, dictating the order and magnitude of what it affects.
If cast at the right time, an abjuration spell can be the difference between escaping unharmed, or death. Most wizards learn atleast a few choice abjuration spells - those who don't tend to not get far in their studies or adventures. Those who specialize in the subject often find employment in noble courts, tasked with ensuring that others, especially other mages, are unable to interfere.
Conjuration
Manipulation of Position
Conjurers call on faraway entities, controlling their whereabouts in space and time. Perhaps the flashiest spells in the school are those that summon extraplanar creatures, be they fey, elemental, or fiend. These spells can be dangerous, as you never know what will answer your summons.
Spells of the school can also alter the position of the caster or their allies, teleporting them over small jaunts or over great distances. The essence of conjuration magic varies depending on the target of the spell - be that the summoned creature or the caster themselves.
The last major type of conjuration spells are those that call upon a sliver of another plane, momentarily tearing open the Bifrost to call upon its energy. While the effects of spells such as Tidal Wave and Cloudkill are easy to confuse with evocation magic, their mode of operation is wholly different.
Wizards who dedicate themselves to the study of conjuration has an army at their fingertips, often making them power brokers in their own right. The most powerful conjurers can take on alone what would normally challenge an entire adventuring party.
Divination
Manipulation of Knowledge
Users of divination are known by many names: seers, oneiromancers, haruspexes, soothsayers, and fortune tellers. Their magic takes many forms, but always focuses on revealing the truth, be it about the location of something, a course of action, or their current actions. Divination magic uses the power of the caster's magic source to provide this insight, and its essence is usually tinged by this source.
There have been many famous prophecies foretold through the ages, some of which have not yet come to pass.
Enchantment
Manipulation of Mind
The enchantment school might seem benign or merely tricksy at a glance, but encompasses some of the most evil spells, forcing emotions on someone, or completely taking away their free will.
Wielders of enchantment magic can use it for good or bad, but many who give in to the temptation eventually learn that adoration from the empty minds of supplicant followers isn't the same as true admiration.
Evocation
Manipulation of Energy
Possibly the most diverse school of magic, evocation deals with controlling raw energy, able to harness almost all essences. While all magic is difficult to cast, evocation is considered the easiest, but this does not make it inconsequential or looked down on. While conjuration magic only calls upon fire from elsewhere, evocation magic creates the fire from nothing but the caster's power and imagination.
Illusion
Manipulation of Sense
Illusory magic deals in altering the perception of others. It could be as easy as hiding someone from sight with the Invisibility spell, or creating the image of a hostile creature with Major Image, to disguising an entire landscape with Mirage Arcane. These spells are usually tinged with chaotic essence, and so are those that wield them.
Necromancy
Manipulation of Life
The school of Necromancy deals in all types of life energies. While often cited as outright evil, those who practice it say it is maligned and misunderstood. Necromancy spells often have a divine essence, using their power both to open and close wounds, using spells such as Inflict Wounds and Revivify.
Transmutation
Manipulation of Matter
The school of transmutation deals with augmenting and enhancing specific aspects of the target, making them faster, better, or stronger. This school works best when applied to that which is already powerful by itself. The essence of a transmutation spell depends on both what is being enhanced, and what it is applied to.
Transmutation also plays a big role in artifice and the creation of magic items, permanently imbuing the item with essences.