I will give you a new heart and put a new spirit in you; I will remove from you your heart of stone and give you a heart of flesh. And I will put My Spirit in you and move you to follow My decrees and be careful to keep My laws.
A heart of stone can be present in a number of forms, however there is one basic underlying theme that is present.
Knowing that God is calling you to do something, but doing nothing about it.
Whether that is not taking a blind step of faith into a new career, continuing to sin in spite of your convictions, or not spending time with God through prayer and reading His word (or even spending time in His word and prayer, but not truly seeking Him through them).
The promising joy that God has given us is that He will turn our hearts of stone into hearts of flesh. The Spirit that God places in us is none other than His Own, which serves as our Counselor and Guide.
I must say, knowing that God loves me enough to continue chiseling away at my life, even when I've found myself cold as stone, is very humbling.
Stone is heavy and uncomfortable. I'd rather give it all to God so that He can change my heart of stone to a heart of flesh, which is a much lighter (and more enjoyable) load.