Well, don't worry, I will give you context about what's your purpose.
The warriors are the most common class in the world, cause it's versatile and usefull in various aspects.
Alliance
The Alliance warriors can be considered part of the infantry of the faction, there's no an order or organization who control them.
It's interesting, cause the game says that you're a civilian who was recruited for the army of the Alliance cause the rest of the forces are fighting in far away battle grounds and need your help for help you to defend the cities that are part of the Alliance and fight in the name of the High King.
Your purpose is defend the Kingdom of Azeroth and the honor and tradition of the Alliance from their enemies, even the savage Horde.
Horde
It's the same for the Horde, you're a civilian who was recruited for fight in the name of the Horde and in the name of the Warchief for defend all the cities what are part of the Horde. You can see many warriors are trained in the Valley of Trials.
Your duty is to defend the Horde's belief in honor and freedom from any of its enemies, including the unyielding Alliance.
Take your armor, sword and shield and fight in the name of your faction.