The name by which they are usually known—the dynasty is also called Staufen or Staufer or the Swabian dynasty, due to their beginnings in the Duchy of Swabia—comes from German hohen "high"and Staufen, the name of the conical hill in Swabia on which their home castle was built in the 11th century (now in ruins that you can visit; there is a coffee shop near the peak). The family motto was the Latin "Sanguis, Pluma, Saxum"; Sanguis, "blood," referred to family/heritage; Pluma, "quill," meant learning; Saxum invoked the castle and signified strength and protection.
The first person we can ascribe to this family was Frederick, who was made Duke of Swabia in 1079 by Holy Roman Emperor Henry IV. Frederick built the castle on Staufen. The family tree of the Hohenstaufens is complex, with the male members holding one or more titles. You can find a thorough listing and family tree here. Frederick II was one member mentioned in this blog, as were Conradin and Henry VI.
One of the "recurring themes" of the Hohenstaufen dynasty was The Investiture Controversy, the question of who had ultimate authority, pope or emperor? Holy Roman Emperors were crowned by the pope, but did that mean the pope had authority over the emperor? It would be easy to say that the pope had authority over spiritual matters and the emperor over worldly ones, but when the pope is a landowner and the Holy Roman Emperor rules over the country in which the pope resides, does that mean the emperor (or other local secular lord) can make bold decisions that affect the pope?
The end of the dynasty was relatively swift and brutal. Conradin, mentioned above, was only two years old. His regency had to defend Sicily against an invasion by Charles of Anjou, brother of King Louis IX of France, who had been promised the title King of Sicily by the popes who wanted to diminish the Hohenstaufens' influence. (The papacy had promised it to King Henry III of England, but he gave it up.) King of Sicily at the time was Conradin's uncle Manfred, who was killed in battle. Conradin himself was executed by Charles after a later attempt to retake Sicily, and the last of the direct Hohenstaufen dynasty was ended. (Manfred had a son, Henry, who died in captivity.) Charles of Anjou became Charles I of Sicily, and the papacy got what they wanted...they thought.
Of all the rulers that came from the Hohenstaufen dynasty, there is a queen who not only had a place in history, but was immortalized in literature. I'll tell you about her next time.