Solomon's blessing to the people was that God would not forsake them nor abandon them but rather maintain the cause of His people as each day required, and that the people would have a perfect heart with Jehovah, to walk in His statutes and keep His commandments as on that day (1 Kings 8:54-61).
In verse 59 Solomon said, "Let these words of mine, with which I made supplication to Jehovah, be near to Jehovah our God day and night to maintain the cause of His servant and the cause of His people Israel as each day requires." Throughout the centuries God has maintained the cause of His people Israel, exercising His justice for them. When they were wrong with Him, He chastised them and disciplined them through the hands of the Gentile powers, including the Babylonian, Persian, Grecian, and Roman empires. But when these nations went too far in dealing with Israel, God maintained Israel's cause, punishing those who mistreated them.
Behind the physical realm there is the spiritual realm in which God governs the entire universe, executing justice for His people every day as each day requires. God does this for His elect, both for Israel and for the believers in Christ. When His elect make mistakes and offend Him, He will discipline them, using others as an instrument for chastening. At the same time, He maintains the cause of His elect by executing justice upon those who persecute them. For example, Hitler killed millions of Jews without a cause, but God came in to execute His justice over Hitler and to maintain the cause of Israel.
After Solomon blessed the people, he and the people offered a vast quantity of sacrifices as the burnt offering, the meal offering, and the peace offering to God (vv. 62-64). The burnt offering is for God's pleasure; the meal offering is for God's satisfaction; and the peace offering is for God and His people to be one in peace.
Solomon and the people held a feast for seven days and seven more days, fourteen days in all. Then he sent the people away, and the people blessed him as their king and went to their tents joyful and glad of heart for all the goodness which Jehovah had done to David and Israel His people (vv. 65-66).