10:19 Therefore [links exhortation that follows with preceding verses], brothers [an affectionate term], since we have confidence to enter the Most Holy Place [not a physical sanctuary but rather the presence of God] by the blood of Jesus [on the basis of Jesus’ saving work on the cross],
10:20 by a new [cf. 2 Cor. 5:17] and living way opened for us through the curtain [imagery of curtain that hung in the tabernacle before the Most Holy Place], that is, his body,
10:21 and since we have a great [high] priest over the house of God,
10:22 [note three exhortations…]  let us draw near to God with a sincere heart [cf. Matt. 5:8] in full assurance of faith, having our hearts sprinkled to cleanse [Jesus’ blood cleanses] us from a guilty conscience and having our bodies washed with pure water [a reference to baptism, the outward sign of an inward cleansing].
10:23  Let us hold unswervingly to the hope we profess, for he who promised is faithful.
10:24 And  let us consider [reflect on, give careful / thoughtful attention to] how we may spur [provoke, sharpen, incite] one another [there are more than thirty one another passages in the NT] on toward love [for God and others; see Matt. 22:37-40] and good deeds [the behavior that results from salvation; see Eph. 2:10].
10:25 [must do 10:25 in order to accomplish 10:24] Let us not give up [abandon or desert] meeting [“the regular gathering together of Christian believers for worship and exhortation in a particular place” (Reinecker/Rogers)] together [consistently; see 1 Cor. 16:2a], as some are in the habit [custom] of doing [to their peril because “Satan is a pirate looking for a vessel without a fleet.”], but let us encourage [entreat, support; emphasis is on what you can contribute; see 1 Thess. 5:14] one another — and all the more as [strong motivation] you see [live with the urgent expectation of] the Day [of the Lord’s imminent return; see Matt. 24:42] approaching.
Note: The words “meeting together” translate the Greek word “episynagogue.” The prefix “epi” means “in addition to.” Some scholars believe the readers of Hebrews attended the synagogue and “in addition” attended meetings of believers. To neglect the “additional” meetings might indicate that they were slipping back into Judaism.