The player characters are all members of the X-Men, a legal superhero organisation dedicated to following the Xavier Vision by opposing terrorism inspired by genetic differences and by upholding the public good. The PCs are all members of the White team, one of three operational units within the X-Men's San Francisco franchise, and thus routinely participate in the same missions. At present, there are three active X-Men franchises: one based at San Francisco, another at New Orleans, and the third at New York.
At its simplest, the Xavier Vision is to work towards the peaceful co-existence of mutants and non-mutants on this world. It is attributed to Professor Charles Xavier (born 24 November 1930), the famous geneticist and mutant activist who was "outed" as a mutant by investigative journalist Lucas Hamble on 20 February 1991. The other two X-organisations are X-Works (a corporate body dedicated to promoting the issues of mutant rights and mutant equality) and Xavier's School (a private school dedicated to providing educational opportunities for mutant youths).
The world is that of the Marvel Universe: however, the campaign departed from the comics in Uncanny X-Men #180, where the odd machine in Central Park was a trap set by Arcade, and not the Beyonder's portal to take our heroes off to the Secret Wars. That event occurred in the campaign world early in January 1984, and it is now late 1996. Anything that happened to the Marvel Universe in a comic published before or at the same time as Uncanny X-Men #180 definitely occurred in the campaign world: anything after that point may or may not have happened, and may have happened differently if it did.
The modern age of heroes (beginning with Fantastic Four #1) started in 1976. Spider-Man and the Human Torch are both in their late thirties, the original Captain America is in his forties and in (semi-)retirement, and Hank Pym left superheroing for good at the age of fifty to be the Avenger's scientific consultant. The Original X-Men are all thirty-something, except Jean Grey, who was brought forward eight years in time (from 1982 to 1990) instead of dying on the moon as everyone thought. Magneto is dead; Apocalypse is dead, though "That Which Endures" has passed from him to Joshua. The Shi'Ar Empire over-stretched itself when it conquered the Kree in 1989, and a popular revolution succeeded in creating the Galaxian Union the following year. Xavier lives with his partner, Lilandra, somewhere in exile in the Shi'Ar galaxy.