The closed circle of suspects is a common element of detective fiction, and the subgenre that employs it can be referred to as the closed circle mystery. Less precisely, this subgenre - works with the closed circle literary device - is simply known as the "classic", "traditional" or "cozy" detective fiction.
It refers to a situation in which for a given crime (usually a murder), there is a quickly established, limited number of suspects, each with credible means, motive, and opportunity. In other words, it is known that the criminal (murderer) is one of the people present at or nearby the scene, and the crime could not have been committed by some outsider. The detective has to solve the crime, figuring out the criminal from this pool (circle) of suspects, rather than searching for a totally unknown perpetrator.
This type of narrative originated with the British detective fiction. Agatha Christie's The Mysterious Affair at Styles (1920) has been credited as a work that started this trend. Other writers of that period, dating to the first half of the 20th century, a time known as the Golden Age of Detective Fiction (or more general, mystery fiction), reliant on the closed circle and related literary devices include Dorothy L. Sayers, G. K. Chesterton, Margery Allingham, Ngaio Marsh and Americans S. S. Van Dine and Ellery Queen.
Those early closed circle mysteries preferred a common setting: a British country house. The country house was such a common element that it gave another name to what is essentially the same genre and the literary device, the "country house mystery". The persons involved were also commonly part of the upper class. Other settings than the country house are also possible, and many have been used in the closed circle mysteries even by Christie herself: a ship, a train, an island, and so on. Nonetheless, the requirements for this mystery enforce certain limitations on this genre, and make certain settings, particularly those that explain limited access outsiders would have, and characters with certain backgrounds (upper class) - much more common than the others. The numbers of suspects vary, from a group as small as four or five, to all the passengers of a coach or a wagon.
After Second World War the closed circle mystery became less common, as other types of crime novels rose to prominence. Nonetheless other writers have continued to use this device till modern days, for example Rex Stout, Lucille Kallen, Jonathan Gash, Simon Brett.
While the closed circle is a common device in literary fiction, it is a much less common occurrence in real world investigations.