What does Hebrews 7:8 mean?

The reference here is to Melchizedek, to whom the patriarch Abraham paid a tithe (Genesis 14:14–24). Melchizedek is described as both king and priest (Genesis 14:18), and this payment of a tithe symbolizes his superiority to Abraham. Verse 5 made mention of the tithes received by the Levitical priests—but also pointed out that they received these tithes from their fellow Israelites, and as a part of the Law of Moses. Melchizedek predates all of these, and so his tithe is more important. This point is part of the author's overall argument that the priesthood represented by Melchizedek is greater than that of Aaron, symbolizing the superiority of Jesus Christ as our superior means of salvation.

The reference to Melchizedek being "one of whom it is testified that he lives" has to be taken in the context of verse 3. There, it is pointed out that Melchizedek is given no genealogy; symbolically, then, he has neither a beginning or end, and no mother or father. This is not meant to be taken literally, and the Greek phrasing of this passage suggests that it's a figure of speech. The real point is in the analogy: that Jesus Christ fulfills the prediction made through the incident with Melchizedek, as our ultimate High Priest (Psalm 110:4; Hebrews 7:17).