Biblically, the human heart is the place of the emotions, the intellect, and the will. It is the place where we think, feel, and make decisions. It is the most inner part of our being.
When we say that God desires service that flows from the heart, we mean that God wants more from us that just outward conformity to a set of rules, a schedule, or a task list. It means that we serve with with desire that flows from the inner most part of our being.
There are many passages that bear this out. When Moses was taking an offering for the construction of the Tabernacle, God gave him these instructions, "The Lord said to Moses, “Speak to the people of Israel, that they take for me a contribution. From every man whose heart moves him you shall receive the contribution for me." (Ex 25:1–2 ESV) In the New Testament, Paul wrote, "Whatever you do, work heartily, as for the Lord and not for men," (Col 3:23 ESV)
The Lord Jesus Christ made this indictment of the religious crowd of His day, "‘This people honors me with their lips, but their heart is far from me;'" (Matt 15:8 ESV) They went through all of their rituals. They knew the right words to day. But their hearts weren't in it.
It is very easy to fall into outward conformity to spiritual activities, and yet be far from God in our hearts. We can go through the motions of reading our Bibles, praying, attending church, and even serving in some ministry, and yet have little affection and passion in our hearts for what we are doing, and for the God for Whom we are doing it. This can only be a temporary condition, because as human beings we will not do for long that which brings us little or no joy.
Some have concluded the answer is just to stop the spiritual activities until their heart changes. The problem with that reasoning is that the very activities that have become perfunctory, are often the means of grace that God uses to change the heart.
The psalmist shows us that crying out to God to change our heart is what is needed. He prayed things like: "Let the words of my mouth and the meditation of my heart be acceptable in your sight, O Lord, my rock and my redeemer." (Psa 19:14 ESV) and "Create in me a clean heart, O God, and renew a right spirit within me." (Psa 51:10 ESV) "Teach me your way, O Lord, that I may walk in your truth; unite my heart to fear your name." (Psa 86:11 ESV) "Incline my heart to your testimonies, and not to selfish gain!" (Psa 119:36 ESV). The psalmist prayed for the condition of his own heart!
We too need the gracious intervention of our God, to change the condition of our own hearts from time to time. If you find that your heart has become cold, and you are lacking the passion and the joy that you once had, cry out to your Father, confess and ask Him to help you! He is gracious, kind, and He will!