Although the Alliance and Horde encompass most of Azeroth's sentient races, there are still a few that maintain neutrality and independence. They prefer the freedom of answering to no one, but they pay for that freedom with automatic suspicion from both Alliance and Horde factions.
Independence has its advantages. In most cases, the Independent races won't be attacked simply for their affiliation. Independent races can easily work for either the Alliance or Horde as mercenaries, and could eventually become regular employees of one or the other. The downside to this is that regular work for one affiliation may create animosity with the other - and regular work for both could create suspicion on both sides. Independent is the best affiliation, as heroes serve whatever masters they please. If they want no part in a mission, they have no special duty to fulfill it.
Many races on Azeroth have no interest in the problems of the Alliance and Horde. These races ally themselves with no one and are more concerned with their own problems. Without affiliation to the Alliance or Horde, the Independent races have fewer ties and responsibilities, not to mention fewer obvious enemies. These heroes can work as mercenaries for either the Alliance or Horde, or as diplomatic liaisons. Independent races, while not allied to the Alliance or Horde, may still be concerned with them and are frequently affected by them, and they must be aware of the goings-on within the two affiliations.
Independent heroes have more freedom when it comes to adventuring, as they have fewer expectations placed upon them. They are not tied to Alliance or Horde laws and can avoid all the tensions therein. However, neutrality can be dangerous. No one weeps for mercenaries' deaths, and there are few - if any - allies to send out search parties for missing individuals. It behooves the Independents to foster good relationships with at least one major faction.
Many of Azeroth's denizens do not owe fealty to the Alliance or Horde. Some races, such as goblins, blood elves and pandaren, are or were Independent. Many Independent races live and work in harmony with members of both the Alliance and the Horde, and could conceivably join a party of either. A goblin running his merchant shop in Orgrimmar would happily take up arms alongside the Horde to defend his shop.
Independent doesn't mean neutral. Some Independent races are neutral, but others may be aggressive. Independent simply means not part of the Alliance or the Horde. It may also mean they are not part of the other large organizations such as the Burning Legion or Scourge.