Master of One Magic

A character that's the best at what they do, and what they do is magic. Well... a type of magic, to be precise. Whether it's summoning, elemental magic, or just plain old moving stuff, they're simply the best there is.

They're often used as Old Masters from whom The Hero must learn his ultimate powers. The Hero may even learn from several of them. Getting apprenticeship from these characters may comprise a bulk of the story. Of course, there's nothing stopping a writer from making The Hero into a Master of One Magic, although they usually claim that title only through sheer power alone.

If there's any magic-user organization that specializes in one type of magic, you can expect the Master of One Magic to be the head of the group. They're often subject to Crippling Overspecialization, especially if they only rely on the magic they excel at when they can generalize their abilities. Also keep in mind that "magic" doesn't always have to go by that name when adding examples. Enlightenment Superpowers, Ki Attacks, Psychic Powers and the like can be counted as well.

Compare The Archmage, a powerful and learned wizard, which a Master of One Magic often is. Also compare The Red Mage, who isn't a master of any one field but has a nearly unparalleled versatility. Poor Predictable Rock is when someone is dedicated to a single element in a Elemental Rock Paper Scissors universe.

Fanfic
"Velvet Remedy: "Your special gift isn't being limited to only one spell, it's being able to use that spell better then any pony in the last 200 years.""
 * Littlepip from Fallout Equestria has no ability to cast spells like other unicorns, all she can use is telekinesis, an ability innate to all unicorns, but she is very, very good with it, as one of her companions put it.

Literature

 * In Mistborn, each of the Mistings in Kelsier's crew is a master of their particular Allomantic power: Breeze in Soothing, Marsh in Seeking, Ham in being a Thug, Spook in being a Tineye, Clubs in Smoking, and Kelsier himself in Pushing and Pulling.
 * Mistings in general are this; since they have only one of the sixteen allomantic powers (as opposed to a Mistborn, who has all of them), Mistings who take their abilities seriously tend to get very good with them. Full Mistborn, by contrast, are much more powerful and versatile, but generally have less finesse in any given power because they're spred thinner.
 * In the Xanth novels by Piers Anthony, everyone can only do one form of magic; basically, everyone just has one innate magic "trick" they can do. Some have the gift stronger than others, however, and the very strongest person in the land is usually made king. One king was a guy who was able to manipulate the weather; he used horrible storms to kill his nation's enemies, and nobody could pull up a tornado like he could. His successor, Trent, was a master of transformation magic. Humphrey was the best there was at information-gathering magic; if you wanted an answer, you went to him, and so on.
 * In the Codex Alera, everyone (well, almost everyone) in Aleran society has Elemental powers, though most people have access to at least a couple and the nobility have them all, with single-element crafters generally considered fairly lowly. However, there are certain single-element crafters who show that they can do a lot with what they've got- Isana with her watercrafting is the most obvious example.
 * The Icemen are a race-wide example of this trope. They draw Elemental Powers from the same source the Alerans do, but their variant only allows for watercrafting. The fact that they've spent centuries focusing on this element alone has allowed them to do things with it that most Alerans wouldn't think possible, including large-scale weather control and advancing a watercrafter's natural empathy to the point of being practically telepathic.

Tabletop Games

 * Specialist wizards in Dungeons and Dragons gain increased proficiency in one of the eight schools of magic, but permanently lose access to two different schools. So a specialist wizard is a "jack of most trades, master of one". There are also the Red Wizards of Thay, who get even more dedicated power with their specialist school but lose access to a third school.

Video Games

 * The Master Trainers in their respective magical disciplines throughout The Elder Scrolls series.
 * In Disgaea, this is the case for all magic users; they specialize in one elemental damage type or healing.
 * In MARDEK, Annunaki society is composed of seven Schools, one for each of the Annunaki Elemental Powers (air, water, fire, earth, light, dark and aether). The greatest of each school gets a seat on the ruling body, the Governance de Magi.
 * Z Angband has High Mages, a class which only knows one magic school instead of the normal two, but is very good at it.

Web Comics

 * Sarin of The Dragon Doctors is a master of Shapeshifting magic.

Western Animation

 * In Avatar: The Last Airbender, Toph and King Bumi are the best earthbenders, Master Pakku is the best Waterbender, and the best Firebenders are Firelord Ozai (until ) and Jeong Jeong. While Aang is the best Airbender by default of being the only Airbender, he doesn't really count since he can bend all 4  elements.
 * Every Bender is eventually one of these. You can only ever learn one type of Bending, unless you are The Avatar.