In etymology, the process of back-formation is the creation of a neologism by reinterpreting an earlier word as a compound and removing the spuriously supposed affixes.
Not only is the process called back-formation, but also the resulting new word in each case is called a back-formation. For example, the "-ar" ending of burglar may be interpreted as an agentive suffix like the -er of runner, leading to the back-formation burgle.
Many words came into English by this route: donate and execute, for example, are back-formations from the earlier donation and execution. Pease was once a mass-noun, but was reinterpreted as a plural, leading to the back-formation pea; the noun statistic was likewise a back-formation from the field of study statistics. In England the word burgle came into use in the 19th century as a back-formation from burglar (in America burglarize is used).
Sometimes such changes occur in more than one stage. The word utopia, from the Greek for "nowhere", was reanalyzed as eu-topia, "good place"; replacing eu with dys as is commonly done, the word dystopia ("bad place", an ideally horrible world) was coined.
Even though many legitimate English words are formed this way, new coinages are often frowned upon, and are often used for humorous effect. For example, gruntled or pervious (from disgruntled and impervious) would be considered mistakes today, and used only in humorous contexts. (The comedian George Gobel regularly used original back-formations in his humorous monologs.) But burger (and beefburger, cheeseburger, etc., from hamburger) is in common use today though it would have been considered awkward or colloquial as late as the 1940s; and enthuse (from enthusiasm) is gaining popularity, though it is still considered substandard by some today--it will likely be in common use within a few years, particularly in its non-transitive form, "He enthused over the presents."