It's God enabling us by His grace to live the way we ought to live. We live by faith in God and not ourselves. It's absolute dependence upon Him. Yet, there's a distinct correlation between faith and obedience. Both contain elements of the will.
Faith is a volitional choice, while obedience is the outworking action of that choice.
It's easy to say that we love Jesus, but the evidence of our love for Him lies within our obedience to Him. We can sing our songs of love and worship, but if they are not accompanied with obedience to His word then we're just playing some sort of a religious game. To love God is to obey God. Obedience is more than saying that I love someone. It's reaching out through concrete actions to that person.