Order refers to a rank, order of status, lineage, etc. It was a term used in the past in the class system and is rarely used today. In the Bible, it is asserted that one of Jesus' many characteristics is that of a high priest.
However, a high priest must follow the lineage (order) of "Aaron." That is, he must be of the tribe of Levi, but Jesus is a descendant of David, from the tribe of Judah. Therefore, the traditional Jewish position at the time was that Jesus could not be a high priest.
Regarding this, the book of Hebrews asserts that there is another lineage in the order of high priests besides the order of Aaron, and that is the mysterious "order of Melchizedek."
Heb 5:6As he says elsewhere, “You are a priest forever, in the order of Melchizedek.”
Heb 5:10and designated by God to be high priest in the order of Melchizedek.
Heb 6:20where our forerunner, Jesus, has entered on our behalf. He has become a high priest forever, in the order of Melchizedek.
Heb 7:11If perfection could have been attained through the priesthood of Levi (for on the basis of it the people received the law), why was there still need for another priest to come, one in the order of Melchizedek, not in the order of Aaron?
Heb 7:17For it is declared: “You are a priest forever, in the Melchizedek order.”
In Psalms, the expression "order" is used.
Ps 110:4The Lord has sworn and will not change his mind: “You are a priest forever, in the order of Melchizedek.”