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- "For this is what your folk would call magic. I believe; though I do not understand clearly what they mean; and they seem also to use the same word of the deceits of the Enemy"
- ― Galadriel, The Mirror of Galadriel
Magic was a term used by the Hobbits to describe processes and abilities of objects which could not be explained outside of their limited lore and knowledge. For Elves and Wizards, this "magic" was not something special or different from the natural world, just part of it that was not immediately visible, leading to more common categorization of things as "Seen" or "Unseen". The "Seen" aspects of a thing or person are only part of it. Through the power of the One Ring, Frodo Baggins at times saw powerful Elves, such as the High-elf Glorfindel, in their true level of power and radiance that extends into the Unseen.
The effects which could be described as magical were of different natures:
 Divine magic
The Ainur as supernatural beings could alter the world in terms according to their nature. Sauron being a Maia (a lesser Ainu) used his powers to manipulate his slaves and objects. Some of them he taught to the Elves who created the Rings of Power, as well as his slaves, the Black Númenóreans and the Men who became Nazgûl, who used this lore as "sorcery".
Similar magic was the one used by the Istari, the Maiar who came to Middle-earth to help the Free peoples against Sauron. The nature of the Istari was not known to all, and they were known as wise old men. They were called Wizards.
Properly, Men using "magic", even for good, are not termed "Wizards". In Tolkien's mythology, this term is specifically only used for the Order of the Istari, who are of angelic origin. A member of the race of Men wielding magical powers would be referred to as a sorcerer, whether for good or evil.
 Elven magic
The Elves were not supernatural beings and although knew the powers of the Ainur, they did not comprehend the concept of "magic" as used by mortals. The Elves were taught arts and crafts by the Valar in Valinor and could put dedication and love in every thing they wrought. Due to their immortality, Elven smiths could reach high levels of experience in craft and lore.
As mentioned, the Rings of Power were such "magical" objects that would seem supernatural to the regular people; they gave powers of manipulation of the word and invisibility. Other Elven artifacts were the Palantíri or the Lamps of the Noldor, as well as the Mirror of Galadriel. Some simpler artifacts were the river-boats of the Galadhrim and the elven ropes, which seemed to have will on their own.
 Dark magic
Sindarin has two words for dark magic: morgul and guldur, although it is not defined clearly, the element "gul" literally means "lore" or "knowledge". It refers to the divine magic of Sauron used for evil, which could be taught to his followers, such as the powers of the Ringwraiths. Black Númenóreans who entered his service learned dark lore from him and became Sorcerers.
Tolkien also uses the word "Sorcery" and "Sorcerer" in negative context. Sorcery is perhaps the equivalent of the dark magic.
 Dwarven magic
The constructions of Dwarves had significant properties which could be defined as magical. Such example could be the Doors of Durin which opened by themselves by pronunciation of the word "mellon", without visible machinery or other assistance.
J.R.R. Tolkien discussed the operations and moral dimensions of magic in Letter 155 of The Letters of J.R.R. Tolkien. Actually, this "letter" is an unsent part of a draft of Letter 154 which may not have been sent because of lingering questions regarding magic in Tolkien's mind (a note at the end of the draft asked about the magic used by the Númenóreans in making swords).