Nuclear Fallout is the residual radiation left over from a nuclear explosion, and usually refers to the irradiated dust created in the aftermath of a nuclear detonation. As Nuclear War is the theme of a large variety of fictional works (games included), Nuclear Fallout is a prominent theme in such post apocalyptic environments.
In Real Life There are two kinds of fallout; global fallout and local fallout. Global fallout consists of light, long lasting irradiated particles, such as Strontium-90 or Caesium-137. Such isotopes last for a period of time which allows for long range dispersal, whilst still decaying quickly enough to pose a radiological hazard if accumulated in the body in large quantities. Local fallout consists of a huge range of different materials, many of which are highly radioactive, but decay quickly (ie. Barium-140, Strontium-92). Local Radiation is a much larger health hazard to those exposed.
Nuclear weapons, on detonation, are either Ground Burst (detonated on impact with the ground) or Air Burst (detonated mid-air). Both bombs dropped on Japan in the Second World War were Air-bursted. Air-burst detonation will result in a more efficient spread of the energy over a target; the energy released by a detonation is released in a spherical pattern, so detonating it on the ground will mean almost half of the energy is striking a tiny spot immediately beneath where it detonates, almost half of the energy is fired into the atmosphere, lost completely, and only the "ring" around the outside of the detonation will cause destruction at the target area. The energy pumped into the small spot on the ground creates enormous amounts of radioactive fallout - making ground bursts much "dirtier" than air-bursts. Air bursts, by comparison, use the entire bottom half of the energy released in the creation of the explosion (the explosion and shockwave are created by the radiation released super-heating the surrounding gasses in the air, which then expand at a very high speed). Some items that would be targeted by nuclear weapons, such as bunkers and rail-road networks, however, will not be destroyed by air-bursting devices, and as such, must be struck by a ground burst to be effectively neutralized.
The Nuclear accident at Chernobyl, Ukraine, released quantities of radioactive materials into the area, however the levels involved were responsible for few deaths - less than one hundred in total. This is not reflected by media portrayals of the matter, including many videogames. The worst fallout disaster in American history was the Castle-Bravo nuclear test, which was expected to yield a blast of 4-6 Megatons, but instead yielded 15 Megatons, resulting in huge quantities of fallout that were not expected to be produced. In terms of real world casualties, however, it caused very few injuries and deaths.
In Video Games As many games take on a post-apocalyptic setting, Nuclear Fallout can easily become an important theme. It almost never affects actual gameplay, however, and in the cases when it does, it is usually handled in a manner identical to Nuclear Radiation. Usually, nuclear fallout as the result of nuclear war will only be felt in terms of story - S.T.A.L.K.E.R.: Shadow of Chernobyl, for instance, features a large variety of mutants, as does the FALLOUT series of games (which was named after this concept). The effects of Nuclear Fallout are almost always exaggerated, and in almost all fiction, it's mutagenic qualities are played up to allow for a wider variety of enemy tipes in a post-nuclear hollocaust setting. As with Nuclear Bombs, and many other elmements of game design, the Rule of Cool reigns supreme.