This is the central verse in the 101 verses contained in a remarkable group of fifteen psalms called "The songs of degrees" (Psalms 120-134). The central verse in the central psalm of this group is the preceding verse: "Lo, children are an heritage of the LORD: and the fruit of the womb is his reward" (Psalm 127:3). The origin of these psalms and this peculiar superscript has always been uncertain. Four are said to be by David, one by Solomon; the other ten are anonymous.
A reasonable supposition, however, is that they were composed by King Hezekiah, after he had been miraculously healed of a lethal illness. "I will add unto thy days fifteen years," God had said, and gave Hezekiah a miraculous sign as confirmation, causing the shadow on the sun dial of Ahaz to go "backward ten degrees" (2 Kings 20:6, 10). In thanksgiving thereof, the king proclaimed, "Therefore we will sing my songs . . . all the days of our life in the house of the Lord" (Isaiah 38:20).
It is significant that the word for "degrees" is the same in both cases. It apparently means "steps" or "ascents." The shadow miraculously ascended ten steps back up the sun dial after it had gone down, and Hezekiah's life was miraculously extended 15 years. Perhaps, therefore, "my songs" mean the ten songs the king composed in commemoration of the ten degrees. He then added five songs of David to round out the total to 15, corresponding to his added "days of our life." And right at the center was his great testimony to the blessing of children. He was childless at the time, but he had a son three years later (2 Chronicles 33:1) by whom He was able to continue the Messianic line promised to David through Solomon. HMM