Pokérus is an ultra rare disease that occurs 3 in every 65,536 on a wild Pokémon. Pokérus is helpful. It will double the EVs of the infected Pokémon. After a few days the Pokémon will heal automatically, and will have a small dot on his stat page.
EV stands for effort value.
A cured Pokémon will still get double EVs, but cannot infect others.
In order to prevent Pokérus from disappearing, store one infected Pokémon in the PC and it will stay infected forever. (PC stored Pokémon do not transfer Pokérus, but remain infected forever). When you want another infected Pokémon, just take out the infected Pokémon from the PC and put it in your party. The rest of the party will quickly be infected.