Why is one's "quiet time" important? In his Systematic Theology Wayne Grudem says that sanctification is "a progressive work of God and man that makes us more and more free from sin and like Christ in our actual lives." That sanctification is God's work, not ours, is demonstrated through Jesus' prayer for his people in Jn. 17 when he prays that the Father would sanctify us. More specifically we understand that it is the Holy Spirit using the word of God to bring about real conformity to the image of Christ, the restoration of the imago dei in men (Jn. 17:17; 2 Thess. 2:13). We yearn for this change, or growth, because in a way it is a returning home. Our progressive salvation is a return to what we are supposed to be; it is a brighter reflection of the character of God; it is a restoration of our humanity that we actually experience this side of the resurrection. This is something we all want, and are more likely to experience as private worship is a part of our lives.
Knowing that God changes us and uses his word to do it requires us to not only give ourselves to the reading and contemplation of Scripture, but also to submit ourselves to it wholly (read obedience). It would be a mistake to conceive of sanctification as the mere product of a 30 minute devotional exercise where one reads the Bible and prays, but I do believe that the quiet time, or private worship, is the best context in which the work of change begins. This is a time when God speaks to us through his word precisely where we need to hear it. Here the word of God is received by faith and is then, or later, applied to the heart and is effectual to bring about the spiritual growth we need.
This shows the value of private worship beyond what is often offered as a motive: duty. We should spend time with God and his word for the joy of meeting with him and being conformed to his image. When I have my head on right, this is why I wake up and open my Bible. Before sermon preparation, beyond a sense of duty, I spend time with God because it is a part of my hope of becoming more like him.
Much more could be said about the relationship between sanctification and private worship, but for now let's conclude that there is a relationship and be encouraged to seek God in such a time.