Psalm 145, the last of the final collection of eight Davidic psalms (Psalms 138-145), is a grand hymn of praise for God the Great King and His majestic reign and gracious acts-including the deliverance of His people. It serves as the closing frame of the five prayers of David seeking rescue from wicked enemies (Psalms 140-144)--perhaps placed here as grateful and worshipful praise in collective response to God's intervention in all these past situations and His faithfulness to continue intervening (compare Psalms 145:18-20 Psalms 145:18-20  The LORD is near to all them that call on him, to all that call on him in truth.
 He will fulfill the desire of them that fear him: he also will hear their cry, and will save them.
 The LORD preserves all them that love him: but all the wicked will he destroy.
American King James Version×). The hymn also serves to transition to the final five untitled psalms of Hallelujah ("Praise the LORD") that close the book of Psalms (146-150). This psalm is specifically titled a "praise" or tehillah (derived from hallel)--the only psalm so titled. From the plural form of this word, tehillim, has come the traditional Hebrew name for the book of Psalms--Sefer Tehillim or "Book of Praises."
David composed Psalm 145 in the form of an alphabetic acrostic, with each succeeding verse beginning with a succeeding letter of the Hebrew alphabet--with the exception, according to the Masoretic Text, of the letter nun. A number of modern versions, based on other texts, include an additional verse corresponding to this letter after verse 13 (though not numbered as a separate verse). However, this does not appear to be justified. As John Gill's Exposition of the Entire Bible comments: "This psalm is written alphabetically, as is observed on the title of it; but the letter 'nun' is here wanting.... Nor is the order always strictly observed in alphabetical psalms; in the thirty-seventh psalm the letter 'ain' is wanting, and three [letters] in the twenty-fifth psalm. The Septuagint, Vulgate Latin, Syriac, Arabic, and Ethiopic versions, supply this defect here, by inserting these words, 'the Lord is faithful in all his words, and holy in all his works,' as if they were begun with the word Nman, but they seem to be taken from Psalms 145:17 Psalms 145:17The LORD is righteous in all his ways, and holy in all his works.
American King James Version×, with a little alteration" (note on verse 13).
David begins his hymn of praise with a powerful declaration that he will extol (exalt or lift up), bless and praise God every day forever and ever (verses 1-2)--demonstrating an understanding that he himself will live forever to render this worship. He then states the theme of his psalm: "Great is the LORD, and greatly to be praised; and His greatness is unsearchable" (verse 3; compare Romans 11:33 Romans 11:33O the depth of the riches both of the wisdom and knowledge of God! how unsearchable are his judgments, and his ways past finding out!
American King James Version×). David can compose praise from uncountable manifestations of God's greatness: His nature, His creation, His plan of salvation, His dealings with mankind.
In verses 4-12 David mentions a number of ways that praise for God will be promulgated. He starts by declaring that praise for God's awesome works will resound from one generation to the next (verse 4). This is accomplished as stories of God's great acts are taught to succeeding generations. The passing on of such knowledge is primarily the responsibility of parents (compare Deuteronomy 4:9 Deuteronomy 4:9Only take heed to yourself, and keep your soul diligently, lest you forget the things which your eyes have seen, and lest they depart from your heart all the days of your life: but teach them your sons, and your sons' sons;
American King James Version×; Deuteronomy 6:7 Deuteronomy 6:7And you shall teach them diligently to your children, and shall talk of them when you sit in your house, and when you walk by the way, and when you lie down, and when you rise up.
American King James Version×).
Another means of transmitting this knowledge is through the recording of God's acts for posterity, as was done in the Scriptures. In fact, observe next in Psalm 145 the back and forth of "I will meditate" (verse 5) and "Men shall speak" (verse 6a), "I will declare" (verse 6b) and "They shall utter" (verse 7). Modern Bible versions often eliminate these shifts, but they are clearly present in the Hebrew. Perhaps the idea here is that David is declaring God's praises in this and other psalms-which others in later generations will sing and talk about.
David then inserts here God's revelation of Himself through His character, essentially repeating God's description of Himself to Moses as gracious, compassionate, full of mercy or loving devotion, slow to anger, and good (verses 8-9; compare Exodus 34:6-7 Exodus 34:6-7  And the LORD passed by before him, and proclaimed, The LORD, The LORD God, merciful and gracious, long-suffering, and abundant in goodness and truth,
 Keeping mercy for thousands, forgiving iniquity and transgression and sin, and that will by no means clear the guilty; visiting the iniquity of the fathers on the children, and on the children's children, to the third and to the fourth generation.
American King James Version×). Similar wording may also be found in other psalms (e.g., Exodus 86:5 Exodus 86:5
American King James Version×, Exodus 86:15; Psalms 111:4 Psalms 111:4He has made his wonderful works to be remembered: the LORD is gracious and full of compassion.
American King James Version×; Psalms 112:4 Psalms 112:4To the upright there rises light in the darkness: he is gracious, and full of compassion, and righteous.
American King James Version×).
In the next verse (Psalms 145:10 Psalms 145:10All your works shall praise you, O LORD; and your saints shall bless you.
American King James Version×a), David says that all of God's works will praise Him, echoing Psalms 19:1-3 Psalms 19:1-3  The heavens declare the glory of God; and the firmament shows his handiwork.  Day to day utters speech, and night to night shows knowledge.  There is no speech nor language, where their voice is not heard.
American King James Version×, where the evidence of God's creative handiwork in the heavens "declares" God's glory.
And a further method of the transmission of God's praise is through the speaking of His saints--His sanctified people--whose task it is to proclaim His Kingdom and mighty acts to the sons of men, the people of this world (verses 10a-12). This is primarily accomplished today, as the New Testament makes clear, through the Church's proclamation of the gospel of the Kingdom. Yet in an ultimate sense, this may picture the saints, when resurrected and glorified as kings and priests in God's future Kingdom, teaching the gospel to all nations.
Verse 13, it should be noted, stresses the eternal nature of God's Kingdom and dominion. We should realize that Scripture presents God's Kingdom in three ways. In the first two senses it is a present reality. God is particularly the King of His people--both ancient Israel and spiritual Israel, His Church, today. Moreover, God is of course always and ever the King of the universe--Sovereign over all His created realm. Yet for the time being, God permits resistance to His rule. And this brings us to the third, future sense of God's Kingdom. When Jesus Christ returns, He will set up God's Kingdom over all nations, enforcing its laws throughout the world and leading everyone to accept God's sovereignty or be removed. All these senses of God's reign appear in the remainder of the psalm.
Verses 14-16 illustrate God's compassion and goodness as, through His sovereign rule, He helps the needy and provides sustenance for all living things. Note that the word "gracious" in verse 8 is translated from hannun, meaning stooping in kindness to help (Strong's No. 2587, from 2603). In verse 17 the word translated "gracious" is hasid (Strong's No. 2623)--an adjective form of hesed (No. 2617), meaning loyal love or devotion. Indeed, in verses 17-20 we see God's loyal love to His devoted people. He will answer their prayers and save them.
While the deliverance and preservation of God's people in these verses happens today, the ultimate fulfillment of this passage will come with the establishment of God's Kingdom on earth in the future, when the wicked who refuse to come under God's loving authority will be destroyed (verse 20) and David's praise will be part of a vast chorus of all people praising God for all time (verse 21).