Breaking down Hebrews 10:19-22 in three points:
Opening Question: Communion - How do most perceive the word/action?
Opening Answer: Commemorating, remembrance, conviction + repentance, etc.
Commonly overlooked element: Worship (see note on #3)
1) v. 19 - "Having therefore, brethren, boldness to enter into the holiest by the blood of Jesus..." (KJV)
Boldness in Greek implies freedom-based assurance. The key is realizing such freedom stems from sanctification, a vertical displacement from sin on route to holiness. Sanctification, at its core, involves divine separation.
Symbolic representation: the split veil
2) v. 20 - "By a new and living way, which he hath consecrated for us, through [that] veil, that is to say, his flesh..." (KJV)
Communion leads to a consecration before God in acknowledging Christ's death in relation to both personal and corporate sin. Similarly to God's love initiative to man, the Cross was His sanctifying drive, His precedented pursuit for our salvation. In other words, God consecrated to us first (through the broken body of Christ), before we could consecrate back to him. God is always ahead of man's game plan, and communion testifies to this truth.
3) v. 22 - "Let us draw near with a true heart in full assurance of faith, having our hearts sprinkled from an evil conscience, and our bodies washed with pure water..." (KJV)
The first four words of this verse indicate a full-hearted worship posture. "Full assurance of faith" can be interpreted as a reference back to the boldness charge in v. 19. Confidence in Christ's priesthood (perfected by proactive consecration) is portrayed with much inspiring positivity.
But why? Sanctification!
The term "sprinkled" punches the "set apart" theme. God's plan of holy substitution is designed to further remove us from wrongful intentions and immoral motives AND so that we may experience higher levels of purification and cleansing (byproducts from consecrating back to the Lord when we approach His table during communion).