Now we ask the key question, “What did Jesus mean by meekness?” To answer that, let us look at the OT background. Ps. 37:11, “But the meek shall inherit the land and delight themselves in abundant peace.” (ESV)
Why did the Psalmist say it? The reason is found in the context of Ps. 37. The problem of the Psalmist is the complaints of the righteous. In v. 1, the righteous are fretting and envious about evildoers. In v. 7, the righteous are losing faith in God. In v. 8, the righteous are filled with frustration and growing anger. They ask why the wicked prosper while the righteous suffer.
Who are the wicked in Ps. 37? In v. 7, they are powerful people who make evil plans and succeed. In v. 12, they oppress the righteous who are poor (vv. 14-16). In v. 20, they oppose the LORD.
The Psalmist assures the righteous that God is in control. In vv. 17-18, the LORD will break the arms of the wicked. He shall uphold the righteous. In v. 20, the power of the wicked is temporary (vv. 2, 9-10, 35-36).
Then the Psalmist urges the righteous in vv. 3-10. (READ) He adds in v. 11, “But the meek shall inherit the land and delight themselves in abundant peace.”
We go back to our key question. What does Jesus mean by meekness? According to Ps. 37, meekness is trusting God in oppression. Meekness is trusting God to bring forth righteousness and justice. Meekness is waiting patiently on the Lord to act against evildoers. Meekness is refraining from anger against the wicked, while waiting on the vengeance of the Lord against them.
 James Luther Mays, Psalms (Int; ed. James Luther Mays; Louisville: John Knox, 1994), 159.