But he whose descent is not counted from them - Melchizedek. The word “descent” is “pedigree” in the margin. The meaning is, that he was not “in the same genealogy” - μὴ γενεαλογούμενος mē genealogoumenos - he was not of the order of Levitical priests. That Melchizedek is meant there can be no doubt; at the same time, also, the thought is presented with prominence on which Paul so much insists, that he was of a different order from the Levitical priesthood.
And blessed him - Blessed him as a priest of God; blessed him in such a manner as to imply acknowledged superiority; see Hebrews 7:1.
That had the promises - The promise that he should have a numerous posterity; that in him all the nations of the earth should be blessed; see Hebrews 6:12-16.