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 惟有你们是被拣选的族类、是有君尊的祭司、是圣洁的国度、是属　神的子民、要叫你们宣扬那召你们出黑暗入奇妙光明者的美德。

Exodus 19:6 你们要归我作祭司的国度、为圣洁的国民．这些话你要告诉以色列人。

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 所以我们只管坦然无惧的、来到施恩的宝座前、为要得怜恤、蒙恩惠作随时的帮助。

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 所以弟兄们、我以　神的慈悲劝你们、将身体献上、当作活祭、是圣洁的、是　神所喜悦的．你们如此事奉、乃是理所当然的。

Romans 12:2 不要效法这个世界．只要心意更新而变化、叫你们察验何为　神的善良、纯全可喜悦的旨意。

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 所以我们作基督的使者、就好像　神借我们劝你们一般．我们替基督求你们与　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.