This is both a call to worship and praise and a prophetic rebuke.

vs. 1-2, 6 are exhortations which continually cry "Let us" (6 times). We are called to praise, thank, and bow showing our humility before God.

vs. 3-5, 7 give reasons to praise, thank, and bow before God.
 
vs. 7c-11 is a prophetic rebuke quoted in Hebrews 3:7-11 in the NT.

New Testament use of this psalm

Heb. 3:7-4:11 “Christians are like the wanderers in the wilderness, rescued from Egypt (the bondage to sin and death), but not yet arrived in the Promised land (heaven). Accordingly, the author of Hebrews cites Ps. 95:7-11 and encourages his readers not to succumb to temptation and die in the wilderness without ever reaching their heavenly rest” Longman, 341. Heb. 3:7-4:13 “forbids us to confine its thrust to Israel. The ‘Today’ of which it speaks is this very moment; the ‘you’ is none other than ourselves, and the promised ‘rest’ is not Canaan but salvation” Kidner, 343.

Heb. 3:7-11 Introduced with just as the Holy Spirit says- Heb. 9:8; 10:15. Partial quotes are made in 3:15; 4:3, 7.

Some of the plays on words in this Heb. 3-4

3:7 Today- 3:13, 15; 4:7, 7

3:7, 15 Hear- 3:16

3:8, 10, 15; 4:7 Heart(s)- 3:12

3:8, 15 Provoked- 3:16

3:9 forty years- 3:17

3:10 angry- 3:17

3:8 in the wilderness- 3:17

3:11 swore- 3:18

3:11 they would not enter His rest- 3:18

3:11 enter His (that) rest- 3:18; 4:1, 3, 3, 5, 10, 11

Gen. 2:2 God rested- Gen. 2:2
Joshua gave rest- Josh. 21:44; 22:4
David spoke of another rest- Ps. 95:7-11
Jesus gives rest- Matt. 11:28, 29
This is one of the ways Jesus fulfills Psalm 95