Gr. diathēkē (see on Gal. 3:15). This word is rendered both “testament” (Matt. 26:28; 1 Cor. 11:25; 2 Cor. 3:6; etc.) and “covenant” (Luke 1:72; Gal. 3:15; Heb. 8:6-10). In the text under consideration “covenant” would be a preferable translation, because the author is speaking of the new covenant (diathēkē), a subject he develops in ch. 8:6-13. Diathēkē is the word used elsewhere for “covenant.”

Gr. egguos, “a pledge,” “a guarantee.” The word here has the meaning of one who becomes responsible for, or guarantees, the performance of some agreement, here, the “better testament.”

 This name emphasizes his human side (see on Matt. 1:1).

That is, in that it was confirmed by an oath, whereas the Levitical priesthood rested on a temporary command.