"Reputation" is gained with various factions generally either by doing quests for them (via normal quest chains or by repeatable daily quests) or often by purchasing and wearing their tabard in the relevant dungeons/instances.
Reputation has several levels, ranging from Hated to Exalted. Hated means that any of that faction member will treat you as an enemy and attack you on sight, Exalted means that you have attained the highest reputation rank with them and often are able to buy various items from them. It also means that often the price of general goods/repairs via any of that factions members will be reduced based on your reputation level with them.
As you gain higher reputation with a faction, more goods will become available. Factions vary as to what is available to buy - some will not provide any vendors at all, others may have recipes, patterns, companion pets, mounts and/or equipment.
In time, I hope to have a list below of guides to getting exalted with various factions. If you find any good guides, please let me know!!
"Old" Reputation
- Netherwing Reputation
- Sha'tari Skyguard
Cataclysm Reputation
- Guardians of Hyjal (Mount Hyjal)
- The Earthen Ring (Vashj'ir)
- Ramkahen (Uldum)
- Therazane (Deepholm)
- Dragonmaw Clan (Twilight Highlands)
- Hellscream's Reach (Tol Barad)
- Mark of the World Tree Vendors (Firelands)
Mists of Pandaria Reputation (levels 85-90)
There is a "quick fact guide" over on WowHead giving details of all factions and rewards.
- How to find the Pandarian Quartermasters
- Lorewalkers
- The Tillers (information from WowHead)
Legion Reputation (levels 100-110)