The Zone is a shorthand name for what is officially called the Exclusion Zone, the area within a 30 kilometer (19 mile) radius of the Chernobyl Nuclear Power Plant. As part of the response to the Chernobyl disaster, everyone within this area was evacuated, and many places were demolished in order to keep the radiation from building up. Prypiat a typical Soviet city built for plant workers and their families is located inside the Zone of Alienation. Today, the Zone is generally considered safe to visit, although it will take generations for radiation levels in the ground and vegetation to come down to levels acceptable for habitation.
Other than translating as "area", the Zone in Russian is also a slang term for generally all forms of incarceration or specifically for prison colony a.k.a. Gulag. A cursed place where humans and humanity are being gradually destroyed, not by radiation but by horrid conditions and tuberculosis.
In 2006, an unexplained energy emission from the power plant rocked the Zone, creating wild mutations and strange, often lethal anomalies; pockets of space where reality itself is altered. Also in the Zone, mysterious objects that came to be known as “artifacts,” that granted improved abilities to whoever held them. Soon, the area became home to rugged, harsh men who came to be known as stalkers, coming into the Zone to search for artifacts that could then be sold to make money. Until Strelok disabled the brain scorcher, however, the innermost areas of the Zone were inaccessible, and rumors of what could be at the center began to proliferate. One of the most prevalent rumors was that a mysterious entity known as the “wish granter,” that could make even the wildest flight of fancy come true.
In reality, there were a group of men inside the reactor, keeping watch over and studying the Zone. Depending on the player's actions at the end of Shadow of Chernobyl, Strelok either joined or killed those men, leading to the events of Call of Pripyat.
In Call of Duty 4: Modern Warfare.
Fifteen years before the current crisis, a young lieutenant Price was sent into the zone under the command of Captain MacMillan, with the objective of getting to the Pollisya Hotel, which would give the two snipers a perfect viewing angle to watch Imran Zakhaev purchasing nuclear materials and, hopefully, assassinate him. After sneaking into the city of Pripyat, they made their way to the hotel, and then waited a full 24 hours on the top floor before their chance finally came. With MacMillan spotting, Price took aim and fired, the bullet tearing Zakhaev's left arm clean off. Believing that shock and blood loss would finish Zakhaev off, the two made their escape by rappelling down the surface of the hotel and fighting their way through the city. McMillan suffered an injury during the escape that rendered him immobile, but he was still able to provide cover fire for Price as they held off the enemy until they could be picked up at the Pripyat Ferris Wheel.