The narrative: In 2096, a massive anomaly opens up in Kiev. An evacuation and quarantine ensues, and a barricade of gun turrets is erected to destroy the alien creatures emerging from the hole. (Creatures that, as the game conjectures, may exist simply to protect the anomaly from us, rather than existing to hunt us.)
The anomaly itself is composed of a black material that dissolves anything that comes into contact with it, and it cannot be studied (until humans develop "vacuum chambers" a decade after the appearance; these chambers are low-gravity fields that allow us close contact with the material for scientific observation).
100 years later, handfuls of folks who have been left stranded in the "zone" form (sometimes warring) clans. The person in charge behind the scenes is Zinovsky, a scientist with questionable motives who has on occasion massacred his own staff in order to hide (from the government) his scientific investigations into the anomaly, the material that composes it, and how it might be weaponized for his personal uses.
His right-hand scientist, Elena, is actually working against Zinovsky in secret and aids you in your quest to shut the anomaly down for good. This process requires a series of keys--tech developed as a result of the anomaly that you collect throughout the game. There are also "oracles"--altered people who (due to their proximity to the anomaly at its initial appearance) have become blind, and the event changed their internal organs, while inexplicably providing them with an understanding of the universe beyond normal human comprehension. They know what the anomaly really is: An intersection of our world with another...
It might all be goofy, B movie stuff. And I agree: You don't need to know Russian to play the game. But there's no way I would have understood any of this without an English translation. And my time with the game was unquestionably enriched because of it. Otherwise it woud have just been a point-and-shoot affair. Snooze.