Okay kiddo, so a priestly covenant is like a big promise that some important people made a long time ago to God. These important people are called priests and they were in charge of leading religious rituals and ceremonies.
The promise they made was to always follow God's rules and do what he asked them to do. They promised to be good leaders and make sure everyone else knew how to follow God's rules too.
This covenant was really important because it showed that the priests were taking their job seriously and wanted to make sure that everyone was connected to God. It also showed that God trusted them and knew that they would always do the right thing.