pokerus doubles the speed you do EV training, your pokemon get stats from killing other pokemon, upto a max of 127 (63 max in each stat) at level 100, this is propotionatly smaller at lower levels. It's what the Super training thing is giving.
in battles, it spreads to other pokemon in your party (the ones next to them), and after a day in your party, they become unconagious, but stay contagious (which is a good thing) forever in your PC.
Thus what you want to do, is do some wild battles, so it spreads to your pokemon, then put one of them in the PC, and get some pokemon you dont care about, spread it to them, and put back in the PC so you have some people that you can pull out and spread it to all your new pokemon.
Every serious pokemon breeder/trainer wants to have access to pokerus as it 1/2s the time it takes to EV train, and once you have it you can spread it freely, then trade away the carriers you produce for very high returns.
For clarity, there are 2 markers, the one saying "pokerus" and a smiley face that replaces it onces it's stop being able to spread it (after being in your party as the day changes), you want to make sure you never run out of pokemon with that 1st one, and all your party pokemon will end up with the 2nd.