completeness or wholeness: an entire, undivided condition, most often the moral integrity of a person whose character has no hidden fault
At root this word means being whole or complete, and Hebrew stretches that one idea across a surprising range. Applied to a person, it names integrity: a life that is all of one piece, with no gap between the inside and the outside and no double-dealing. This is by far its most common use, especially in the Psalms and Proverbs, where people are said to walk in their integrity or to have integrity of heart.
That integrity is not a claim to be sinless. It describes an honest, undivided loyalty rather than a flawless record. David is repeatedly credited with it even though the same books record his failures. The picture is of a heart turned fully toward God, without a hidden agenda pulling the other way.
The same wholeness shows up in two narrower ways. In a set phrase, to act in one's integrity means to act in good faith, with no scheming behind it: the men who followed Absalom without knowing his plot went in their innocence, and the soldier who shot the fatal arrow drew his bow without aiming at anyone in particular. In a few places the word keeps its plain sense of full extent or peak condition, as when disaster arrives in full measure or a person dies in the fullness of vigor.