1 Peter 2:5,9 You also, as living stones, are built up as a spiritual house, to be a holy priesthood, to offer up spiritual sacrifices, acceptable to God through Jesus Christ. But you are a chosen race, a royal priesthood, a holy nation, a people for God's own possession, that you may show forth the excellencies of him who called you out of darkness into his marvelous light.
Believers in Messiah Yeshua (Jesus) have all been inducted into a priesthood by the new birth, a New Covenant priesthood established by the Lord Himself, in the order of Melchizidek [Psalm 110:4; Hebrews 7:11]. While the Old Testament Levitical priesthood was limited exclusively to the sons of Aaron, all New Testament believers in Messiah are called a "Royal priesthood" [1 Peter 2:5; 2:9].
Exodus 28 describes the exquisite beauty of the holy clothing to be worn by Aaron and his sons. Anyone beholding these men in full priestly dress would be struck with wonder and admiration at the beauty and significance of this majestic, bejeweled array of garments. The impression created by the Levitical priests and their sacred adornment could be likened to the New Covenant believer's outward appearance, which should also be obvious to others; the beauty of good works, tenderheartedness, joyful countenance, etc.
Yet there is another parallel, perhaps even more important: when dressing himself for his priestly ministry, the Levitical High Priest actually begins by donning his linen undergarments. These, of course, are invisible to others, yet are the garments closest to his body, and could be likened to his invisible inner life.
Yeshua's Sermon on the Mount speaks to this invisible area of human nature and its propensity to sin. We may appear quite religious and lovely outwardly, impressing others with cultivated behavior, and good deeds, while our "undergarments" are soiled and anything but holy. But, of course, the undergarments of the High Priest were also required to be holy, even though no one would ever see them.
Your outer life and behavior will reveal a great deal about you, as your face and actions reflect your heart, character, and values. But the source of all that is visible in your life must correspond to that which is hidden...your "spiritual undergarments"; i.e. your inner life with the Lord. The holiness of God should permeate every facet of our lives, so what we walk out in public flows from our private communion with Him.