Who were the Perizi during Avraham Avinu's time and why there was a quarrel between them?

They are simply one of the 7 Cananite nations who were in the Land of Israel before we came. The Ibn Ezra (Shmot 3, 8) identifies them as coming from Tzidon, the son of Canaan. Some say their name refers to their type of settlement, Paruz= open cities without a protective wall. Other's say their name infers that they worked with metal. The quarrel was between Avraham's shepherd's and those of Lot, and had nothing to do with the Perizi, although some explain the combination of the two issues into one verse, because the Perizi spread their settlement precisely at the time of the quarrel.