It doubles the EVs, or Effort Values, that you gain. Note that this does not include EVs gained by Super Training. Just in case you don't know what EVs are, I'll explain.
Effort Values are attributes which give bonuses to an individual Pokemon's stats and improve differently depending on what Pokemon they defeat.
This means that each Pokemon gives different Effort Values, generally based on their highest stat. Geodude give off Defense Effort Values. It takes 4 EVs to increase a stat by one point, and a Pokemon caps at 252 EVs in one stat, and 510 in total.
For example, let's say I have a level 1 Torchic who I want to have a high Attack stat. I look up which Pokemon give Attack EVs, an example being Bellsprout. For every 4 Bellsprout my Torchic defeats, it gains 1 Attack point.
Pokerus doubles this quantity. If my Torchic has Pokerus, it will gain 8 Attack EVs instead of four, making its Attack stat go up by 2 points rather than 1 after defeating 4 Bellsprout. Note that the EV caps are still the same.