Although ESO makes no distinction between the schools of magic, Rollplay still needs some way to quantify a character's magical strengths. To that end, the system uses the schools of magic as they appear in later games to determine spell typing. Understanding the schools of magic and what they are capable of allows players to use their magical toolkit more effectively and creatively.
It should be worth mentioning that while the system can adapt to a wide variety of spells, there are certain buffs/debuffs and other effects that won’t work. Such things can, however, be acted out in the form of roleplay if the GM allows it.
"Spells in this school change the world around the caster so normal physical truths no longer hold. It is sometimes confused with Illusion magic, as both schools seek to change normal truths. Illusion magic, however, is not bound by the laws of nature but Alteration magic is. The power of Alteration comes from the fact that the nature of its changes applies to all, whereas Illusion magic affects only the caster and the target." — UESP
Alteration includes a variety of shielding spells, the ability to walk on or breathe under water, and movement through air. The school can also grant the caster the power to make things (including themselves or other people!) feel heavier or lighter, as well as assist them in handling locked objects. Those that are skilled enough in Alteration may also paralyze their opponents.
"Conjuration magic is the art of summoning creatures or items from another plane. It is one of the six colleges of Magic, but is not considered to be one of the 'great schools' by the Mages Guild... Despite this, it has been practiced for centuries by witch covens and wizards throughout Tamriel. Clan Direnni's sorcerers were some of the first to formalize the rituals, chants, and incantations used to open a connection with the plane of Oblivion, many of which are still standard centuries later." — UESP
Conjuration includes the ability to summon creatures, weapons, and armor from another plane of existence. Skilled conjurers may also be able to banish Daedra, turn the undead away from them, or in more taboo practices... Reanimate corpses.
"It is concerned with dealing damage to all forms of matter, both living and non-living, and with making matter more vulnerable to such damage. Mastery of Destruction magic may bring a certain amount of danger." — UESP
Destruction magic includes, but is not limited to, elemental attacks such as the commonly known fireball, spark, or ice shard spells. Mages specialized in the School of Destruction can also apply a number of weakness to their foes, disintegrate weapons and/or armor, and even drain resources. These attacks have a variety of range, from a simple touch to a massive widespread area of effect depending on the skill and power of the mage casting these spells.
"It is similar to Alteration magic in that it seeks to change the world around the caster so normal physical truths no longer hold, but while Alteration magic is bound by the laws of nature, Illusion magic is not. Its weakness comes from the fact that while Alteration affects the entire world, Illusion magic affects only the caster and the target. Illusion spells can change a target's visibility, produce or remove light, produce or remove noise, charm a creature, induce hatred in it or calm it down, enhance or remove a creature's courage, prevent a creature from seeing or moving, or allow the target to see even in total darkness." — UESP
Illusion magic is known to grant the caster the ability to instill a range of different emotions in their target, from calming someone or rallying them, to making the individual cower from fear or go on a hate fueled rampage. Those with knowledge of Illusion can also grant themselves the ability to see in the dark temporarily with night eye or by creatinglight out of nothing, illuminating themselves or a target, or casting total darkness to conceal themselves... but why do that when you can make yourself partially or completely invisible, which is also an example of Illusion magic? In addition to all of this, sound can also be created from an unknown source to serve as a distraction or muffled entirely to help sneak by a group of enemies.
"[The school] least understood by the magical community. The art has been described as allowing a mage "to alter the nature of magic itself" and as involving "the manipulation of magical forces and boundaries to bypass the structures and limitations of the physical world." The spells in the school have their origins with the Psijic Order of Artaeum, who call their study the "Old Way", and the school has occasionally been referred to as the Way of the Psijic. The practice of Mysticism seems to require dealing with "conundrums andparadoxes" and abandoning logic to "embrace a temporary sort of insanity" which may lead the student to long-term harm if practiced without proper instruction. Its usage was common among the mystic Reachman shamans during the Second Era." — UESP
Mysticism is more than just trapping souls in soul gems. It can grant the caster the ability to detect life, to mark a location and recall to it to escape an otherwise dangerous situation, and to move things with the power of telekinesis. Mysticism can also be used to dispel harmful effects, or to reflect physical and/or spell damage back at an enemy, as well as silencing other casters and absorbing spells to regain Magicka.
"The Restoration discipline is the mastery of the spell effects of the College of Restoration, but it is not considered to be one of the "great schools" by the Mages Guild. Restoration spells heal, restore, and fortify the body's attributes and abilities, cure disease, and protect it from other malign influences. The primary spells of this college heal wounds, cure disease, and restore lost vitality, but can also augment strength, endurance, intelligence, agility, and other bodily attributes. Absorption skills are also sometimes considered part of this college, although they may also be classed as Mysticism magic." — UESP
Restoration, in simple terms, grants the caster the power to heal wounds or remove harmful ailments, such as disease or poison. This magic can also be used to bolster one’s resistances. Restoration is not limited to the caster. It can be used to aid their allies.