The professed Jewish believers in Christ whom the author of Hebrews addressed were in danger of turning back from following Him. To prevent them from turning away from Christ, and possibly going back under the Old Covenant, the author sets out to show the superiority of the New Covenant. It is better in every way than the Old Covenant. It has a superior Mediator; it has a better priesthood; it was established on better promises; it has a better sacrifice. And in Hebrews 9, the author shows that the New Covenant has a better tabernacle.
The earthly tabernacle constructed under the Old Covenant, and for its worship was the place where God dwelt with His people (9:1-10). But no one had direct access to Him! Only the high priest and he only once a year could enter the presence of God. And those who worshipped there could never be perfect in regard to the conscience. Their conscience could never be completely cleansed! The people always had a consciousness of their sin and guilt. But Christ Who ministers as High Priest in a greater and more perfect tabernacle (9:11), cleanses by His blood, the blood of the New Covenant, the consciences of all of believe in Him (9:14)!