The Pokérus is a microscopic life-form that may attach to Pokémon.
When infected, a Pokémon's status screen will indicate it much as it does any other status condition (with icon being different for Generation III and IV, while Generation V has the same as Generation IV and Gen II having no icon at all). When another normal status condition, such as Sleep, affects the Pokémon, the Pokérus icon will be replaced. As long as the Pokémon is infected with Pokérus, it can spread the virus to the other Pokémon in the player's party. The infection may spread if the infected Pokémon is in the main party after a battle. An uninfected Pokémon must be next to a Pokémon infected with Pokérus in the main party for the virus to spread. If Pokémon that have already been infected and cured from Pokérus are in the main party and are on either side of a Pokémon currently with the disease, Pokérus will not spread after any amount of battles. Pokémon that are put into the PC will keep the status indefinitely. From Generation III onward, Eggs may catch Pokérus like any other Pokémon.
Once a Pokémon's immune system has fought off the virus, they cannot spread it further, nor can it be spread to them by other Pokémon. In Generations II and III, a dot will appear on the Pokémon's status screen to indicate that they have had the virus previously, while in Generation IV and V, it will be a small smiley face. Though the virus is gone, its positive effects will remain, most specifically the ability for that Pokémon to gain double EVs.
Any Pokémon on the player's party at the moment the system clock reaches midnight after a certain number of days in that position (number of days depends on the strain and generation) will become immune. An easy way to keep a "vessel" for future spreading is to always send the infected Pokémon to the PC, Day Care, Stadium 2 (in Generation II), Pokémon Box Ruby & Sapphire (in Generation III), or My Pokémon Ranch (in Generation IV) before midnight. The game also recognizes immunizing if the system is turned off and on again on the next day.