This little verse has a lot of theology packed into it. And it starts with the first word: create. I'm inclined to think that my heart is naturally clean, and I just sully it up a bit when I make mistakes. But here is implied quite the opposite: on its own, my heart is unclean, and the only way to get a clean one is an act that only God can perform. The verb here, בּרא, is the exact same verb used in Genesis 1:1 when God created the world from less than nothing. If my heart is to be renewed, then an act of divine creation—creation as in the Book of Genesis—is needed.
And then there's that second clause. Is it simply a repetition of the first clause in slightly different language? From a Christian perspective, it looks like something else. Whereas the first clause is about justification—that is, forgiveness that makes me right with God—the second part is about what happens after that, i.e. sanctification. The first clause is a momentary act when God cleanses my inward being; the second clause is the rest of my life as I grow into the new creature I have become.
By the work of your Son on the Cross, O God, create something new within me: forgive me and make me clean. Then, by the indwelling of your Holy Spirit, cause me to become what I already am in your eyes. Amen.