Being intended as an online cooperative game only, Umbrella Corps does not offer much in terms of plot. It is instead gameplay focused, like many of Capcom's mobile games.
Two years after the Global Bioterrorist Attacks and twelve years after Umbrella's collapse in 2003, the corporation's viral samples and research data were ransacked and sold on the black market. Consequently, bioterrorism has spiralled into global threat. By the game's setting in 2015, the resulting viral outbreaks being too numerous for even the B.S.A.A. to contend with, entire districts have been simply locked down and abandoned. Within these districts, independent "Zombie Hunters" commit illegal activities for their own reasons [note 1]
The search inevitably brings these corporations into direct conflict with other corporations which are also seeking the same things; either by heir intents on gaining sole rights to vaccines or underground bio-terror networks looking to increase the range of their B.O.W. merchandise. As a result, these global corporations send mercenaries into several infested and infected locations to search for viral samples, research data and lost secrets.
New additions to canon
New conclusions to previous games are made in Umbrella Corps. It is heavily implied that Neo-Umbrella experimented with the C-Virus in the Antarctic Base ruins previously seen in Resident Evil CODE:Veronica. In the aftermath of Resident Evil 4, it is revealed that villagers previously forced out by Los Iluminados returned home by ignoring the quarantine, becoming parasitised by surviving Plagas. The Type 2 Plagas developed by TRICELL are shown to have survived the BSAA infiltration of the Kijuju Autonomous Zone. In another conclusion to Resident Evil 5, it is revealed that TRICELL's headquarters fell to a bioterrorist attack involving zombie dogs.
↑(in the English backstory it is referred to as a "sport" conducted by thrill seekers, though the Japanese leaves it vague).