We're all familiar with the words and music of this song. We sing it often. But this should be something that we pray to God about on a regular basis. We should definitely be praying for a purer heart, but more specifically, we should be praying that God help us remove the "secret sin" from our life...
Most likely, there are things about your life that not everybody knows about... and some of those things may be weaknesses that only you and God know about. Let's face it, it's very easy to sin when nobody else is around. We think that nobody will find out about it. - That's what Satan wants us to think. Truth is, God knows about it - and that should be more embarrassing to us than any of our friends/family finding out about it.
Defeating our secret sins is something we need to be avidly trying to do. Obviously one of the most effective ways to do this is prayer. If there's something that you're struggling with in your life, pray to God about it. But don't just pray when you're lying in bed - say a prayer out-loud to God - being specific about what you're struggling with. It helps to hear yourself say it.
Another thing we need to take advantage of is our Christian brethren. We are so blessed to know so many people who will lovingly support us. We often think that we can't tell anyone about our struggles because they might look down upon us or laugh at us - that is not the case. James tells us in James 5:16 to "Confess your trespasses to one another and pray for each other - that you may be healed." We hesitate to talk to others about our personal struggles, but if we hope to get better - this is something that can definitely help.
We tend to not worry too much about our personal sins - since we're the only ones who know about them... But secret sin does just as much damage to us and is something we have to get out of our lives.