Just as you used to offer the parts of your body in slavery to impurity and to escalating wickedness, so now offer them in slavery to righteousness leading to holiness.Romans 6:19
In the biblical sense, a slave is someone who does not have any ownership rights of their own; they belong to another. In a primary respect, the life of a believer is simply an honest recognition that the life they are living is not their own. Everyone serves a master, whether sin or God; we are simply choosing to follow God.
The life we are living should be voluntarily offered back to the One who provides it to us in the first place. This is so simplistic, it is almost inconceivable. Unfortunately, we are so used to viewing our lives as belonging to ourselves that we easily fall back into old practices of doing whatever we want with them. We many times unwittingly go back to serving impurity and wickedness out of habit.
However, a believer, in the process of being freed from sinfulness, accepts another intentional yoke upon themselves, a yoke that is bearable and easy. This is because it is a life being lived as the Designer has created it to be: a life separated to Him. We recognize that all life flows from God and we are simply yielding ourselves to live within the parameters of the life that he has given us.
A life that is set apart in holiness is separated because it is constantly being renewed in the image of the One who made it. Our mindfulness in remaining intentionally and purposefully bound to this life is what causes us to become holy and set apart for use by God.