faction is a group of people that share same interests. Many of the factions in Azeroth are not involved in the on-going tensions between the Horde and Alliance and, thus, are generally open to members of both sides. These "non-aligned" factions can provide you with information, equipment, and experience. Other factions are actively involved in the disputes between Alliance and Horde and are thus open only to members of one of those two sides. These factions are often attached to the various battlegrounds.
You change your status within a faction by gaining (or losing) reputation. Additionnal information on reputation is found here.
Below are some of the factions currently in the game:
Non-aligned Factions
on-aligned factions tend to stay out of the problems between the Alliance and Horde. Whether they stay out for higher purposes, such as fighting against evil in general, or out of self-interest, such as making a mint of money; all that is important is that non-aligned factions are open to all.
The Argent Dawn
Some say that it is always darkest just before the dawn. Whenever darkness falls, the light of hope will drive away the shadows; wherever the forces of evil work in secret, the brave men and women of the Argent Dawn will be there to thwart their dark designs. The Argent Dawn is an organization that makes no distinction between Alliance or Horde, but instead tries to unite the people of Azeroth in the fight against evil.
War is brewing in the distant lands of Silithus. All over the world, men and women are gearing up for one final push into the heart of the Qiraji empire to end the threat which has been lying in wait, barely contained behind the barrier erected by the Night Elven druids and the mighty dragon Anachronos during the climactic battle at the end of the War of the Shifting Sands. Ever since that fateful day, the members of the Cenarion Circle have kept a close watch on the wastes from their base at Cenarion Hold at the center of northern Silithus.
A gathering of the exotic from around the world and beyond, Silas Darkmoon has brought together the Darkmoon Faire as a celebration of the wondrous and mysterious found in Azeroth. While the Faire spends most of its time in parts unknown, they do stop from time to time in Mulgore and Elwynn Forest. When the faire is on its way, barkers will stop by Orgrimmar and Ironforge to announce its arrival.
The Searing Gorge is home to a group of exceptionally stout dwarves who have split from the Dark Iron clan. On the cliffs overlooking the region called the Cauldron, in the far north of the Searing Gorge, the dwarves of the Thorium Brotherhood have established a base of operations, Thorium Point. From here, they keep a close eye on the Dark Iron dwarves’ activities in the Searing Gorge and beyond. Adventurers seeking out Thorium Point will find that the dwarves of the Thorium Brotherhood hold great rewards for those who aid them in their neverending struggle against their former brethren.
With the Burning Legion defeated, the Timbermaw furbolgs have recently taken their first, careful steps outside of the safety of Timbermaw Hold. They are wary of all strangers, fearing that they may mistake them for their corrupted brethren and attack. However, the Timbermaw are painfully aware that they will not last on their own; adventurers who seek out Timbermaw Hold in northern Felwood and prove themselves as friends of the Timbermaw will learn that the furbolgs value their friends above all else.
The Zandalarians were the earliest known trolls, the first tribe from which all tribes originated. Alongside the other tribes, the Zandalar defeated the blood god, Hakkar, and cast down his priests, the Atal'ai. However, as the Atal'ai priests have returned and the threat of Hakkar hangs once more, the Zandalar tribe has arrived on the shores of Azeroth to battle Hakkar once again. They offer what assistance they can to those who help them in their fight against the Atal'ai and Hakkar...
When the Titans first descended on Azeroth, vanquishing the Old Gods and bringing order to the world, the Highfather of the Pantheon himself empowered the great dragon Nozdormu with some of his own cosmic powers, enabling the dragon to guard time itself and police the ever-spinning pathways of fate and destiny. And so, the stoic, honorable Nozdormu became known as the Timeless One. Ever since then, Nozdormu's Brood has guarded the timestream from all who would seek to disrupt its flow, guided by the Timeless One's wise, all-knowing counsel.
attlegrounds factions are not only attached to either the Horde or the Alliance; they are also attached to their specific battleground. In order to gain reputation with a particular battleground faction, you will have to complete quests inside that faction's preferred battleground and turn in tokens from that battleground. For instance, the Frostwolf Clan will only accept tokens from members of the Horde who have gone into Alterac Valley.
Alterac Valley Factions
After Thrall's triumphant uniting of the clans, the Frostwolves, now led by the Orc Shaman Drek'Thar, chose to remain in the valley they had for so long called their home. In recent times, however, the relative peace of the Frostwolves has been challenged by the arrival of the Dwarven Stormpike Expedition.
The Stormpikes have set up residence in the valley to search for natural resources and ancient relics. Despite their intentions, the Dwarven presence has sparked heated conflict with the Frostwolf Orcs to the south, who have vowed to drive the interlopers from their lands.
Arathi Basin, located in Arathi Highlands, is a fast and exciting Battleground. The Basin itself is rich with resources and coveted by both the Horde and the Alliance. The Forsaken Defilers and the League of Arathor have arrived at Arathi Basin to wage war over these natural resources and claim them on behalf of their respective sides.
Warsong Gulch is the battleground of the Warsong Outriders and the Silverwing Sentinels. The two factions wage war against each other from their respective holds of Warsong Lumber Mill and Silverwing Hold. The goal of their war is to lay claim to Warsong Gulch by capturing their enemy's flag and returing it to their own base. By aiding them in their struggle, adventurers can get various rewards, as well as honor and the esteem of one of the two factions.
faction is a group of people that share same interests. Many of the factions in Azeroth are not involved in the on-going tensions between the Horde and Alliance and, thus, are generally open to members of both sides. These "non-aligned" factions can provide you with information, equipment, and experience. Other factions are actively involved in the disputes between Alliance and Horde and are thus open only to members of one of those two sides. These factions are often attached to the various 
on-aligned factions tend to stay out of the problems between the Alliance and Horde. Whether they stay out for higher purposes, such as fighting against evil in general, or out of self-interest, such as making a mint of money; all that is important is that non-aligned factions are open to all.
attlegrounds factions are not only attached to either the Horde or the Alliance; they are also attached to their specific battleground. In order to gain reputation with a particular battleground faction, you will have to complete quests inside that faction's preferred battleground and turn in tokens from that battleground. For instance, the Frostwolf Clan will only accept tokens from members of the Horde who have gone into Alterac Valley.