אתה כהן לעולם על דברתי מלכי צדק
Most (non-Jewish) readers say this means (something like) "You are a priest forever after the order of Malkizedek" (Malkzedek is a King of Salem who gets a very brief mention in Genesis.)
Nachaum Sarna (a Jewish reader) also takes it this way, and explains that this mention of an "order of Malkizedek" suggests that a longer story about the king, and perhaps his order, was once known in Israel and that the psalmist is referencing material (perhaps biblical material?) now lost.
Rashi takes it differently, reading the verse: you are a priest forever because of the speech of Malchizedek but his ensuing comment obscures more than it makes clear:
From you will emerge the priesthood and the kingship that your children will inherit from Shem your progenitor, the priesthood and the kingship, which were given to him. דִבְרָתִי מלכי-צדק. The “yud” is superfluous, like (Lam. 1: 1): “the city that was once so populous (רבתי).” Because of the speech of Malchizedek, because of the command of Malchizedek. You are a priest, Heb. כהן. The word כהן bears the connotation of priesthood and rulership, as (II Sam. 8:18): “and David’s sons were chief officers.For instance: (1) If the yud is superfluous, why is it there? (2) When did Malkizedek say anything about the future kings of Israel? What command did he give?
Alter (also a Jewish reader) (I think) goes a third way, writing that the reference to Malchizedek is a pun (the word means "righteous king") He takes the verse as "you are a priest forever, by my solemn word, my righteous king." He sees no reference here to any lost literature and, unlike Rashi, no reason to depart from the plain meaning of the words.