What does it mean Melchizedek was without father, without mother, without descent…? (Hebrews 7:3)

The word ‘without descent’ here (Greek ἀγενεαλόγητος agenealogētos) is an adjective really meaning ‘without genealogy’. So the issue is that Melchizedek was not given any genealogy in Genesis.

He is without father or mother or genealogy, having neither beginning of days nor end of life, but resembling the Son of God he continues a priest forever. (Hebrews 7:3 ESV)

This is an important contrast with the Levitical priests who had to be of descent from Aaron on the father’s side. It was also considered an advantageous qualification for a high priest to be descended from Aaron on the mother’s side as well – as was John the Baptist, whose father Zechariah and mother Elizabeth were both able to show genealogies tracing back to Aaron himself on each side.

The point being made in Hebrews 7:3 is that Abraham deferred to a priest who was not dependent on genealogy – Melchizedek.