The biblical teaching about 人人(Chritians) 皆祭司 is found in 1Peter 2:9. What the nation of Israel (see Exodus 19:6) failed is taken up by Christ's Church (meaning all Christians).

1Peter 2:9 惟有你們是被揀選的族類、是有君尊的祭司、是聖潔的國度、是屬　神的子民、要叫你們宣揚那召你們出黑暗入奇妙光明者的美德。

Exodus 19:6 你們要歸我作祭司的國度、為聖潔的國民．這些話你要告訴以色列人。

What do we Christians as royal priests do then? First, like OT priests who brought themselves as well as people before God's throne of mercy in the temple for forgiveness of sin through sacrificial offerings, we Christians as royal priests are commanded (Hebrews 4:16) to come readily and as often as needed before God's throne of mercy for forgiveness, grace and timely help. See also 1John 1:9.

Hebrews 4:16 所以我們只管坦然無懼的、來到施恩的寶座前、為要得憐恤、蒙恩惠作隨時的幫助。

No longer will we need to go through some other human intermediary (such as a Catholic priest who hears people's confession as a go-between between sinners and God) to repent and get right with God. See 1Timothy 2:5 and Hebrews 4-10. Any sinner can come directly before God for forgiveness and mercy. Martin Luther was clear about this point.

Second, unlike the OT priests who repeatedly offered animal sacrifices for the forgiveness of sin, Christ the Great High Priest has offered himself up as a sin offering once for all of us (see Hebrews 4-10). Like OT priests who served God in the temple, we Christians (meaning, imitators of Christ) as the royal priests are commanded (Romans 12:1-2) to offer our own bodies as living sacrifices to serve God in a holy and pleasing manner in the community of faith (which is the Church).

Romans 12:1 所以弟兄們、我以　神的慈悲勸你們、將身體獻上、當作活祭、是聖潔的、是　神所喜悅的．你們如此事奉、乃是理所當然的。

Romans 12:2 不要效法這個世界．只要心意更新而變化、叫你們察驗何為　神的善良、純全可喜悅的旨意。

Third, like the OT high priests who pleaded for forgiveness before God on behalf of Israelites, we Christians as royal priests are commanded (2Corinthians 5:20) to act like Ambassadors of Christ by proclaiming Christ (see the second half of 1Peter2:9) and helping to bring other people into reconciliation with God through Christ.

2Corinthians 5:20 所以我們作基督的使者、就好像　神借我們勸你們一般．我們替基督求你們與　神和好。

To sum up, we Christians as royal priests are (1) to come before God directly and readily for mercy and forgiveness, (2) to offer our bodies as living sacrifices in serving God, and (3) to act as Ambassadors of Christ in helping other people to reconcile with God through Christ.

The second function as royal priests will last through eternity since after we are resurrected with a new heavenly and incorruptible body we will serve God forever and ever.

The first and third function will help ourselves and others to reconcile with God and get into the glorious eternal home in heaven.