The Knights Templar were one of a number of military monastic Orders in the medieval period. They were a religious Order, with the difference that their work was not farming but killing God's enemies. Templar belonged to a monastery-castle known as a Preceptory or Commandery with its own master, responsible to his Provincial Master or Grand Prior, and ultimately to the Grand Master. The hierarchy was slightly different in the Holy Land (since it was principally involved in fighting, while in Europe the main activity was financial management and recruiting.
The Templar uniform, white with a red cross, is the most common image of a crusader knight. However, the crosses of each military order were different, the one we see here is not historically correct in relation to any order of the period.