What does Psalm 40:8 mean?

This is connected to the verses cited in Hebrews 10:5–7, which applied this passage to Jesus the Messiah. As do many New Testament citations, this uses the Septuagint translation, in Greek. Phrasings between that and the Old Testament Hebrew are often different. The Hebrews reference shows that God's ultimate intent for our salvation involved a physical body, fulfilled in that of Jesus Christ (Psalm 40:6).

David was thrilled to do God's will, whom he knew personally as "my God." He also held God's Word in his heart. His devotion to God's will and God's Word pictures Jesus' relationship to God and His Word. When the Devil tempted Jesus for forty days and forty nights in the wilderness, Jesus refused to abandon His worship of the Father by falling down to worship the Devil. The Devil took Jesus to an exceedingly high mountain and showed Him all the kingdoms of the world and their glory. He promised to give Jesus all the kingdoms and their glory if Jesus would down and worship him (Matthew 4:8–9). But Jesus resolutely refused the offer. He rebuked the Devil and appealed to the biblical command: "You shall worship the Lord your God and him only shall you serve" (Matthew 4:10). Jesus continued that pattern throughout His earthly ministry (John 4:34; 5:19; 17:4–6).