What that means is that it has the Pokerus virus, which doubles EV gain. It will stay saying "PKRS" for about a day, meaning that it can infect other Pokemon with the virus if you use it in battle with other Pokemon in your party. After about a day though, the "PKRS" label will change to a smily face, meaning that it can't infect other Pokemon with Pokerus anymore, but still has the effects of it itself. If you want it to stay infectious longer, you can put in a box, and take it out only when you need to infect other Pokemon with it.
As for why you're other Pokemon don't have it right off the bat, it's because Pokerus is gotten from battling a wild Pokemon that has the value for it selected to "yes," the chance of which happening is extremely low. You most likely only battled it with only one of your Pokemon, and tha's why only the one has it right now. When you took it to the Pokemon center after taht, Nurse Joy should have mentioned that one of your Pokemon have Pokerus.
And if you don't know what EVs are, here's a good article on it:
http://www.serebii.net/games/evs.shtml