What does Psalm 18:27 mean?

In this context, being "humble" is a reference to having a low position or status, as well as an attitude which recognizes one's limitations. The Lord saves poor or afflicted people, but He often acts to bring down the arrogant. He saved David when David was afflicted, but He defeated Saul, David's arrogant adversary.

Around the dawn of human history, Lucifer, a shining angel near God's throne, became haughty. He looked arrogantly at God's throne and decided to capture it for himself. He said in his heart, "I will ascend to heaven; above the stars of God I will set my throne on high; I will sit on the mount of assembly in the far reaches of the north; I will ascend above the heights of the clouds; I will make myself like the Most High" (Isaiah 14:13–14). The Lord responded: "But you are brought down to Sheol, to the far reaches of the pit" (Isaiah 14:15).

All who follow the example of Lucifer will ultimately find that sinful pride goes before a fall. James 4:6 assures us that "God opposes the proud but gives grace to the humble." James 4:10 promises those who humble themselves before the Lord that the Lord will exalt them.