After passing through Route 13 and seeing (and maybe catching) Cobalion, you find Lacunosa Town to the northwest.
Meet Professor Juniper and Bianca
When you go south toward the Pokémon Center in Lacunosa Town, Professor Juniper and Bianca will appear. Professor Juniper takes the two of you north to a house where an old lady tells you about Giant Chasm. Professor Juniper mentions that the road to the Chasm is blocked right now.
The old woman says that the Chasm was created by a giant meteorite that had a scary pokémon inside. It is said that this pokémon will appear when darkness falls over the land. When this pokémon appears, is causes a cold wind that freezes everyone around, and then it eats pokémon and people. This is why Lacunosa Town has a wall around it and there is a rule not to go out after dark.
Professor Juniper and Bianca go outside. Follow them to hear them discuss the pokémon in the old tale, which Bianca says is even more powerful than Unova's legendary Dragon. Professor Juniper will tell you about this legendary Dragon if you want (she talks about Zekrom if you're playing Black 2, or Reshiram if you're playing White 2). She believes that the meteorite is the same as the stone from which the legendary Dragon was revived, which may be a connection between the Dragon and the pokémon from the old lady's story. Bianca says that this means that the pokémon from the story must be very powerful.
Professor Juniper asks you to ask Drayden if he knows anything. He's a Dragon trainer and is the mayor of Opelucid City, just past Lacunosa.
Get Items
If you go west from the house where you heard the story from the old lady, you find some stairs. Go up, then east. There's a house here. Talk to the guy to get a Berry, then pick up the Metronome to the right of him.
Back outside, go all the way west, then south. Look for the Full Heal to the left of the building. Then you can go east to reach a vending machine and some stairs down to the Pokémon Center.
Help Hugh
If you go west from the Pokémon Center, you find Hugh. He'll ask if you've seen Team Plasma around here. Then Zinzolin and a Team Plasma Grunt show up. Hugh will challenge them and ask you for help. He'll ask if you're ready yet. If not, say no and go prepare, then go back and talk to Hugh.
My recommended pokémon for the upcoming double battle are Litwick/Lampent/Chanedelure (resistant to Ice, strong against Fire) as your first pokémon, then have Cobalion, Magnemite/Magneton/Magnezone (resistant to Poison), and Drilbur/Excadrill in your party. Hugh will fight by your side using his level 43 starter.
After the battle, Zinzolin and the Grunt will run off to Opelucid City, and Hugh will run after them.
Move on to the Next Route
When you're ready to move on, go west to reach Route 12.