It is called Exp. Share, short for "experience share"
To be able to get it you must do these things:
After you get the Devon Goods from the bandit, and head back to Rustboro, the Devon employee will take you to Mr.Stone, the president. He will ask you to deliver the Devon Goods to Captain Stern in Slateport City. He will also give you a letter for his son Steven, who is in the Dewford cave.
He will give you your PokeNav in advance, as a way of thanks for delivering the Devon Goods.
When you deliver the letter, go back to Rustboro, and talk to Mr. Stone again. He'll give you one Exp.Share.