Verses 5-6 are likely some of the most quoted and well-known verses in all of Proverbs. Trust in the LORD with all your heart. This has some key principles that come with it. First, trust and belief are connected but not the same thing. Many people believe that God exists. Not nearly as many actually trust in God. Use an example of a chair. I can say that I believe that the chair will hold me up if I were to sit on it. But I show I trust the chair when I actually sit down and let it do what I believe that it can do. In a similar way we say we believe that God can do this or that. But we demonstrate trust when we actually place it into His hands and let Him work.
We also need to be aware that there are many cultural ideas that go with the idea of "following your heart". If you heart is not trusting and dependent on Jesus, then your heart can actually lead you astray. I have known people who have "followed their heart" and abandoned their wives and children for something or someone that makes them happier (only leading to despair and heartache for themselves down the road). God would not tell someone to do this. Instead, that is what leaning on your own understanding looks like. We can't let our hearts and emotions lead our lives, rather we must allow Jesus to lead our hearts and make our paths straight.
We must think about God in all aspects of our lives. In all our ways we must acknowledge Him. This is a reminder that we cannot separate our "spiritual lives" from the rest of our lives. All aspects of our lives, not just Sunday mornings need to come under submission to Jesus, and we must think about how I honor God at work, at home, in recreation, in my family, in my friendships.