A Royal Priesthood

When the new covenant was established on the cross, the veil in the temple was torn, and we gained direct access to God.

Then, behold, the veil of the temple was torn in two from top to bottom; and the earth quaked, and the rocks were split.
- Matthew 27:51 (KJV)

We essentially became priests.

But ye are a chosen generation, a royal priesthood, an holy nation, a peculiar people; that ye should shew forth the praises of him who hath called you out of darkness into his marvellous light; Which in time past were not a people, but are now the people of God: which had not obtained mercy, but now have obtained mercy.
- 1 Peter 2:9-10 (KJV)

Royal means "having the status of a king or queen or a member of their family".

A king has authority (to rule with Christ), and a priest has access (to God). We have both.

And hath made us kings and priests unto God and his Father; to him be glory and dominion for ever and ever. Amen.
- Revelation 1:6 (KJV)

And hast made us unto our God kings and priests: and we shall reign on the earth.
- Revelation 5:10 (KJV)

We will also reign with Christ (as co-heirs) during the 1000 years.

And I saw thrones, and they sat upon them, and judgment was given unto them: and I saw the souls of them that were beheaded for the witness of Jesus, and for the word of God, and which had not worshipped the beast, neither his image, neither had received his mark upon their foreheads, or in their hands; and they lived and reigned with Christ a thousand years.
- Revelation 20:4 (KJV)

This is a reference to the fact that we will judge the world, and the angels. Judging is a form of kingship.

Do ye not know that the saints shall judge the world? and if the world shall be judged by you, are ye unworthy to judge the smallest matters? Know ye not that we shall judge angels? how much more things that pertain to this life?
- 1 Corinthians 6:2-3 (KJV)