What does Hebrews 7:24 mean?

Unlike the priests of the Old Covenant, Jesus will not see His priesthood end in death. The men who served as priests and high priests could only intercede for the people while they were alive. After death, their personal priesthood ended and their priestly responsibilities had to be passed on to others. This passage is all about the ways in which Jesus' priesthood, in the style of Melchizedek, is superior to the Levitical priesthood. Verses 23 and 24 highlight this issue of mortality—which Jesus does not suffer from. Unlike human priests, Jesus has an "indestructible" life, or an "eternal" life (Hebrews 7:16). This not only makes Jesus' priesthood superior, it allows Him to fulfill the promise, made by God in Psalm 110, to establish a priest like Melchizedek "forever" (Psalm 110:1–4).

Other limitations of the Levitical priesthood are discussed in this book as well. Priests are naturally sinful (Hebrews 7:27), while Christ is not (Hebrews 4:15). Their sacrifices are limited (Hebrews 9:6–7), while the sacrifice of Christ is perfect and infinite (Hebrews 9:11–12). These limitations prevent the Old Testament Law from saving us completely, since the system is based on human efforts. The purpose of these laws was never to save us, but to point towards the one who could utterly save us—perfectly and completely—through His superior role. This person is Jesus Christ.