Horde is a co-op mode where you will partner with a Crew member to take on waves of enemies. Aside from being in a Crew, you'll also need a Thumper - which you can collect from Gear Packs or purchase from the store.
When you initiate a Horde battle, you'll be prompted to select a Thumper before you can send an invite to your whole Crew. Once a crew member accepts the battle will start with the first wave. Make your way through the waves and defeat the Boss to earn rewards.