While certain parts of the Catholic Church hierarchy have changed and adjusted to meet modern demands, in some ways it still retains a medieval "flavor."
This is especially the case with cardinals, who are frequently called the, "princes of the Church."
Why is that?
What is a cardinal?
First off, it is important to know what precisely a cardinal is and where that position came from. According to the Catholic Encyclopedia,
“By the term cardinal (cardinalis) was originally understood every priest permanently attached to a church … It became the usual designation of every priest belonging to a central or episcopal church.”
The Latin root of the word is cardo, meaning “hinge,” and reflects their pivotal role in the original formation of the Church. We hear an echo of this root today in the fact that every parish priest must be incardinated into, or officially attached to, a diocese.
Especially in Rome, the first “cardinals” were priests assigned to specific regions/churches within the city. This term was also extended to deacons who assisted these priests in Rome, “For the care of the poor the city was divided into seven regions, each of which was administered by a deacon.”
As the centuries progressed, the pope was in need of more help in administering the growing Church and appointed certain regional bishops to be cardinals. These cardinals would be appointed in strategic locations and would often travel to Rome as a local representative to help the pope in making important decisions.
Over time the cardinal's role increased and since the 12th century, nearly all of the popes have been chosen from the rank of cardinals.
This tradition is one of the primary reasons why cardinals have been labeled "princes of the Church." A prince in medieval culture would typically be the next in line to rule in place of the king. If a king died, a prince would likely take his place.
Technically popes do not have to be chosen from the cardinals, but this hasn't happened since the 14th century.

