The verb dierchomai is a common verb of motion meaning to pass through or go through a place. In the Gospels and Acts, it frequently describes Jesus's and the apostles' travels — going through towns and regions proclaiming the gospel. In Hebrews 4:14, it describes Christ as having 'passed through the heavens,' establishing the basis for bold access to God.
The theological depth of dierchomai is most evident in Hebrews: our great High Priest has 'gone through the heavens' — not merely into the earthly Holy of Holies as the Levitical priests did, but through all heavenly spaces to the very throne of God. This cosmic traversal of Christ is the basis for the believer's confidence in prayer. What Christ has passed through, He has opened as the way for us.