This verse uses a comparison from lesser to greater (see study note on Hebrews 9:14). Just as heaven is greater than the earthly tabernacle, Christ’s sacrifice had to be much better than earthly sacrifices.
copies of the heavenly things: See study note on Hebrews 8:5.
heavenly things to be purified: Just as the tabernacle needed cleansing because of the Israelites' sin (Leviticus 16:16–19), the heavenly tabernacle required removing uncleanness from those entering heaven under the new covenant.