Pokérus is a VERY rare occurrence in the Pokémon games, implemented since GSC.
Its effect? Pokérus doubles the Effort Points (EVs for short.) earned when you defeat a Pokémon in battle. Maybe you need a bit of info on this? If yes, let me know...
In short, Pokérus allows the infected Pokémon to grow their Stats further when training. It appears randomly in wild Pokémon, and getting it to infect your Pokémon is way rarer than finding a Shinny Pokémon (More than 1 in 8192 chances...).
Pokérus wears off one day after the Pokémon remains in your Team. If you deposit infected Pokémon in your PC, the Pokérus won't wear off. However, having the Pokérus Status in your Pokémon just allows it to be passed on to the other Pokémon in your Team (Just battle or walk... it'll eventually spread on your Team.). After the Pokérus wears off, you'll notice a small dot in their left Box of the Stats screen. This dot means that the Pokémon can't spread Pokérus anymore, but still has the Effort Points it gains in battles doubled.
Hope this helps.
EDIT: BTW, if you Trade a Pokémon with Pokérus to FR/LG, the Pokérus Status will never wear off due to the lack of internal clock in such game. However, the Virus won't spread. It'll only spread in Ruby, Sapphire or Emerald Versions. The infection capacity will wear off after one day in each of those versions, though.