Horde Expedition is the combined forces of the Horde in Northrend, which are:
These four factions are sub-factions to Horde Expedition. When you gain reputation with one of these four factions, half of the reputation earned will count towards your reputation with the Horde Expedition. This means you will need to be either exalted with two of these sub-factions in order to be exalted with Horde Expedition, or you can have the equivalent amount of reputation spread across the four.
By raising your reputation with the Horde Expedition, you will get exclusive treats such as the Schematic: Mechano-hog. This mount is probably the main reason for most people to raise their reputation with the Horde Expedition, though you will have to have the Engineering profession maxed out in order to make it.
If you get exalted with the Horde Expedition you will also get the achievement The Winds of the North.
The Horde Expedition is abit special. While you have to wear Championing Tabards in dungeons in order to gain reputation with other factions, you gain reputation with the Horde Expedition by not wearing a Championing Tabard in dungeons.
You can easily become revered with Horde Expedition just by quesing in Northrend. A thing worth mentioning is that you will gain most of your reputation by questing for the sub-factions of the Horde Expedition, as there are few quests given directly by Horde Expedition NPCs. Beyond average questing, you can do a handful of daily quests that will raise your reputation with the Horde Expedition. These are:
Grizzly Hills (PvP Daily)
Icecrown
Here's a guide on how to do the Grizzly Hills PvP Daily quests. For the Icecrown Quests, there are no specific guide, but I suggest you go to this guide and pick out the parts you need. Just Ctrl + F and write the quest name of the quest you want to do, and you'll jump to the relevant parts in the guide for that quest.
There are two Horde Expedition quartermasters. There is Gara Skullcrush in Borean Tundra (41,53) and Sebastian Crane in Howling Fjord (79,30).
Here are very many good pre-raid items, aswell as the famous Schematic: Mechano-hog.
Revered
Charged Wand of the Cleft - Isn't the best wand out there, but it works.
Darkspear Orb - A good Off-hand for PvP survival.
Sin'dorei Recurve Bow - Can be used while building up gear, but it's not really recommended to use. There are several better Ranged weapons which are just as easy to get.
Warsong Punisher - Again not recommended to use. Go with Hammer of Quiet Mourning instead.
Warsong Shanker - Quite good starting dagger in both PvE and PvP.
Warsong Stormshield - Good for Holy Paladins, aswell as Resto & Elemental Shamans.
Exalted
Arcanum of the Savage Gladiator - Great head enchant for PvP survival.
Plans: Titanium Plating - For tanks mainly.
Schematic: Mechano-hog - A must have for you who like to show off. It's really expensive though.