The Humans and Orcs have been at odds with one another for several generations now. In the course of their battles, they have enlisted the aid of various other peoples. What was once a tension between two peoples is now a tension between many different cultures on one of two alliances. One of these is simply called The Alliance, and the other is The Horde.
After Medivh opened The Dark Portal and Orcs began to enter the Kingdom of Azeroth, the Humans led by King Llayn were under siege by several of the different orc tribes. The conclusion of the first war found the orcs destroying Stormwind Keep and the remaining humans fleeing Azeroth.
Even with the Kingdom of Azeroth fallen, there were several other surviving human kingdoms. They, along with the Dwarves and High Elves, recognized the threat the orc Horde represented, and formed the Alliance.
After acquiring technological assistance from the Goblins and strength of arms from the Ogres, the Horde poised itself to strike Lordaeron and Gilneas. Making their beach head in the northern parts of Azeroth, they made their own alliance with the Forest Trolls. Although the Horde was driven back during the second war, the Forest Trolls would eventually leave the Horde, and the Goblins would seek neutrality to sell to the highest bidder, the beginning seeds of the Horde had been sown, and the Alliance was already well-formed.
The Horde and Alliance, in various incarnations, have done battle during the scope of three wars. Toward the end of the third war, they were even forced to work with one another to stop the Burning Legion. In spite of this, and an uneasy pact between the Human mage, Lady Jaina Proudmoore, and the Orc warchief, Thrall, afterwards, there are very strong seeds of tension between the two factions and they will frequently enter skirmishes with one another. Many of the best-known hotbeds of conflict are the battlegrounds, but there are certain other regions where competing interests have led to Horde and Alliance fighting each other. At best, it could be said that there is a truce between the two factions.
As it stands now, the Horde consists of the Orcs, Tauren, and Trolls of southern Kalimdor, and the Forsaken and Blood Elves in the northern end of the eastern continent. The Alliance races include the Humans, Dwarves, and Gnomes of the Eastern Kingdoms, and the Night Elves and Draenei who now both dwell in off-shore areas along the northwest coast of Kalimdor.
There are a great many other cultural groups within the World of Warcraft. Some are friendly toward players, and others are hostile. The two groups that get their own section of the Reputation Window are the Steamwheedle Cartel and The Sha'tar. Any other "factions" in the game would be among exclusively hostile groups such as The Scourge or the Silithids.
See also: Reputation