Thrallmar and Honor Hold are two of the first factions you will encounter as you venture through the Dark Portal for the first time, as they are the army that has been sent by the Horde and Alliance to deal with the threat in Outland.
There are many ways to gain reputation in The Burning Crusade, and the order in which you complete these steps can make things slightly easier and ensure you do not run out of quests before you reach exalted.
The simplest way to earn reputation is to complete any dungeon in the Hellfire Citadel. If you are leveling you can complete Hellfire Ramparts and The Blood Furnace as they have around a level 60-63 requirement.
Killing NPCs reward the reputation in dungeons, and these two will stop giving reputation at 5999/6000 Friendly.
If you are level 69-70 you can choose to run The Shattered Halls as these mobs will reward reputation all the way until Exalted.
Quests reward a high amount of reputation in Outland and are a very fast way to earn reputation if you are level 70 and have a fast flying mount.
One of the reasons many players opt to dungeon grind their way to level 70 is for this reason, as completing quests at max level rewards extra gold instead of the experience you would have received and you still gain reputation.
Small "deliver this" style of quests will award 75 reputation and most go out and kill X quests will award 250 reputation, with elite quests awarding up to 1000 reputation.
Only quests tied to the Thrallmar and Honor Hold hubs will award reputations with these factions, and once players continue to Falcon Watch or Temple of Telhamat, the reputation will change.
Why farm Reputation in the first place? Well, the first reason is you will want to unlock the heroic versions of the dungeons.
The Flamewrought key that unlocks the three dungeons in the Hellfire Citadel at heroic level can be purchased from the Quartermaster.
There are also weapons and gear that can be purchased such as the Marksman's Bow, that hunters will be after early as it is close to the best they can get outside of raid drops.
Specific profession recipes and patterns are from different reputation vendors so this is another reason players will be farming reputation, such as leatherworkers who will be after the Nethercobra Leg Armor pattern.