The setting of Call of Cthulhu is our world ... or mostly so. Typically the time and place is New England of the 1920s. Playing in other eras (up to the present) is possible, and the protagonists may travel of course -- sometimes to places that are not on this earth. The players take the roles of ordinary people, drawn into the realm of the mysterious: detectives, thieves, scholars, artists, war veterans, etc. Often happenings begin innocently enough, until more and more of the workings behind the scenes are revealed. As the characters learn more of the true horrors of the world and the irrelevance of humanity, their sanity inevitably withers away.
It is quite common for a player character to die in gruesome circumstances or end up in a mental institution, and players must often start with a new character. While arguably being more realistic, it also makes it hard for players to bond with their character.
For the limited time they stay healthy, characters may be developed still. Call of Cthulhu does not use levels but is completely skill-based.
The name of the game stems from Cthulhu, a so called old one purportedly sleeping in a hidden place.