Anagrams are a form of letter play where the letters in words, or phrases, is scrambled.
An anagram is a puzzle device facet that rearranges the letters of a word, or multiple words, to create new words.
For example, the word "heart" can be re-arranged into "earth". In this example, the word "heart" is called the subject, and "earth" the anagram. In puzzle, a player will encounter the subject and be expected to find the anagram, which we will the answer in this context, to distinguish from the general idea.
Anagrams have a degree of "perfection" based on the allowances in the mapping from the subject to answer. There is no agreement on what "perfect" means here, but it can play a role in the difficulty of a puzzle.
For example, the word "grape" can be transformed into "pager" by simple rearrangement of the letters. Whereas "earliest" can transform into "arise late" if you allow for adding a space, and "planchet" can change to "can't help" if you allow for a space and apostrophe.
Languages that use accents, ligatures, or other combining features may allow for modification of those features. For example, in French, "Noël" and "Léon", the accent on the "e" has changed, as well as the capitlization of the first letters.
When used among other facets in a puzzle device, the more "perfect" an anagram is, the clearer it will be for the player. Leniency will result in players uncertain of their answers, or wondering if they've found all the pieces. Though adding templates, or other clues, can alleviate these problems. For example, given the word "trample", a player could be given another puzzle piece with "???_????", or a picture of a mountain goat, to help them find "ram pelt".
The answer may be associated to the subject in addition to being an anagram. For example "vile" and "evil" have a direct association in their meaning, whereas "listen" and "silent" have a complementary assocation.
Anitgram is sometimes used to refer to anagrams that have a contradictory, or opposite, meaning. Examples include "Satan" rearranged to "Santa" or "funeral" rearranged to "real fun".
Other anagrams may form associations in larger phrases. For example, "the flea ate the tea leaf" where "flea ate" and "tea leaf" are anagrams.
Finding associated anagrams can improve the perceived quality of a puzzle. It can also improve a player's response to the puzzle. Associated words are good feedback that a player has found the right one, whereas completely unrelated words may leave the player feeling confused, or unimpressed.
Anagrams necessarily rely on lingual qualities, thus require knowledge of the language used. As translation of the subject changes the available letters, the anagram will also have to be changed.
It would interesting to know if there are actually any translatable anagrams, such that the translation of the subject and answer remain anagrams in the target language. That is, excluding the trivial case where the words are the same in both languages.
Though we usually think of words and phrases as the subject in a proper anagram, we generally consider any scrambling to be the same type of device. Using our first example, this ordered set of letters "aehrt", though not a word, is still a subject with the anagram "earth".
There are many popular games that involve this type of scrambled letters, such as Scrabble and Boggle. In these types of games a player isn't required to use all of the avaiable letters, but can chose subsets to form a word.
In puzzles, each letter may be an individual puzzle piece. Instead of having an explicit order, the player is expected to unscramble the pieces to find the correct word.
If you have any questions, need an example, or want clarification, then let me know. Ask on Discord or Twitter.
Assume everything in this reference is a working draft, there's prone to be some mistakes and inconsistencies. I figure it's best to publish and get feedback rather than write for years in secret. The terms will change, the structure will shift, and the bugs will be chased out. It'll take a while.