Teach me your way, O Lord, and I will walk in your truth; give me an undivided heart, that I may fear your name. (Psalm 86:11)(NIV)
Throughout the Psalms, the word heart refers to the center of the human soul or spirit. From this center flow all a person's emotions, thoughts and attitudes. An undivided heart means that these expressions reveal a heart that is pure and unselfish, not corrupted in any way (Ps. 24:3-4).
The prophet Jeremiah wrote in a similar vein, telling us that God wants us to return to him with all our heart (Jer. 24:7). He called this concept singleness of heart and action (Jer. 32:39). Ezekiel also spoke of God giving an undivided heart and ....a new spirit (Ezek. 11:19).
Only God can give someone an undivided heart; it's not something we get on our own. Still, we must accept God's offer; we must want an undivided heart. The surest way to know whether one's heart is undivided may be to echo David's prayer: Search me, O God and know my heart; test me and know my anxious thoughts (Ps 139:23). Only God can tell whether or not our hearts are pure.
(from the Quest Study Bible published by Zondervan)