An anagram is a word or phrase that has had the letters rearranged to make another word or phrase that uses all the letters of the original. It is very common to use anagrams as crossword clues in British newspapers. Anagrams are very ancient and probably originated from people looking for the inner meaning of words or names. They were very common in ancient Rome. Today they are a hobby or a pastime. A good anagram should be related to some quality or property of the original word or phrase.
For example: If you rearrange the letters of "Margaret Thatcher" you get "That great charmer."
If you rearrange "Dormitory" you get "Dirty Room".