After you rescue the Herdier, the owners ask you if you trained with Alder. You haven't done that yet, so you should go back to Floccesy Town and visit Alder.
Train with Alder
Go south to exit Floccesy Ranch, then go south through Floccesy Town. Alder will meet up with you and see that you gave the Town Map to Hugh. Alder sees that you have already grown a lot since your visit to the ranch, so he asks you and your pokémon to help him.
Before going into Alder's house, go to the left side of the house to find an X Speed.
In the house, Alder asks you to battle the two kids.
The first is School Kid Seymour. The pokémon that he has depends on which starter you picked. It will always be the type that your starter is strong against. If your starter pokémon is Snivy, he has a level 9 Panpour. If your starter is Tepig, he has a level 9 Pansage. If your starter is Oshawott, he has a level 9 Pansear.
After the battle, Alder will heal up your pokémon.
Next you have to battle School Kid Cassie. The pokémon that she has will be the type that your starter is weak against. If your starter is Snivy, she has a level 9 Pansear. If your starter is Tepig, she has a level 9 Panpour. If your starter is Oshawott, she has a level 9 Pansage.
Afterward, Alder talks about type matchups. He also mentions that if a pokémon uses a move that is the same as its type, the move will be more powerful.
Alder will heal up your pokémon again after the battle.
Meet Mr. Medal
Now you can go outside. A mysterious man named Mr. Medal will give you the Medal Box. He will ask if you have heard of the Medal Rally. It doesn't matter how you answer, because he explains it either way. You get medals for completing different achievements.
Mr. Medal gives you six hint medals, which give you a clue about how to receive the different medals that are available.
Whenever you achieve something worthy of a medal, Mr. Medal will be in the nearest Pokémon Center and will give you the medal.
Mr. Medal tells you to use the medal box to learn more. Then Mr. Medal departs.
Alder comes out and mentions that a new Gym Leader has arrived in Aspertia City, so you should go there and test your abilities.
Be sure to use your Medal Box, because you will find a manual inside that explains how it works.
Go Back to Aspertia
Now you should go back to Aspertia City to meet up with that Gym Leader that Alder mentioned. On the way, Alder will stop you and give you some Oran Berries, explaining how to use them.
Go the rest of the way to Aspertia City.