During the medieval period in Europe the political power of the kings and great nobles was often constrained by the actions of who?

To a large extent, this was done by the pope and the church. The popes could and did excommunicate kings, and when they did it often gave licence for other people to overthrow those kings, and certainly meant that the kings' supporters were no longer obliged to help or support them.

The kings and great nobles were constrained to a large extent by lesser members of the nobility. For example, the lowest order of nobility at the time of King John of England was the barons. But it was the barons who forced King John to sign the Magna Carta.

The common people also were a constraint to some extent. The willingness of the people of London to support one monarch or another was particularly important. They were possibly decisive in the war between Steven and Matilda over the monarchy.