A parcel of land given by a noble to a lesser noble in exchange for loyalty and money in the Middle Ages was called a (n).

It was called a fief

Explanation:

A fief is a piece of a land that is entrusted or given to a lesser noble (known as a Vassal) by a high ranking noble (or lord). The land is used by the vassal to cultivate food which sustains and support his household.

In return, the vassal is obliged to be loyal to his lord and even fight for him as a knight. It is important to note that this practice is a form of European feudalism that existed during the middle ages.