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.