Enter the house across the fossil Lab and talk to the woman there. This is a daily event where she'll ask you to show her a Pokemon with a speed above the value she requires. You don't have to show her the actual pokemon itself - as long as a Pokemon in your party exceeds / meets her expectations, she'll be satisfied. You'll obtain a Wing item. This is a consumable item that raises your Pokemon's EV point.
Health Wing | Increase HP EV by 1 point |
Muscle Wing | Increase Attack EV by 1 point |
Resist Wing | Increase Defense EV by 1 point |
Genius Wing | Increase Special Attack EV by 1 point |
Clever Wing | Increase Special Defense EV by 1 point |
Swift Wing | Increase Speed EV by 1 point |
Pretty Wing | No EV increase |
Source: Serebii.net