Though the exact nature of the Plague is never explained in the game, fans have speculated about its progression.
The Plague results from human exposure to nanites created by Capek. It is thought that when such nanites enter a human body, they begin to attack the brain. The attack stops all non-essential neuro-muscular functions, causing the victim to fall to the ground and making them unresponsive.
It is at this point that the nanites proceed to replicate, systematically taking over the entire body of the victim. Some nanites appear to over-replicate, producing tumor-like bulges on the victim's body. The victim's body and immune system will either accept the nanites -- leading to severe mutations -- or reject the nanites, resulting in death.
Curing the plague is fairly straightforward; in Capek's own words, all that needs to be done is stop the replicators. This is done by administering an antidote.