When David wrote this chapter of Psalms he was actively being sought after by King Saul. This must have been a very difficult thing for David to deal with. It wasn't too many years earlier that the prophet Samuel had annointed David to be the king of Israel. David knew he was the rightful king. Yet it was Saul who was sitting as king and who was hunting down David to kill him.
Nevertheless, David trusted in God. You see David knew what the outcome was going to be. He knew who his God was and that the God of the Bible never lies. King Saul could not kill David for God would not make a promise and then fail to follow through. David was not on the throne yet, so David could not be killed by Saul.
Therefore, David makes a freewill offering to God because he knows that God's promises are true and faithful. David has faith in his future because he knows the God that controls the future.
We can have that same peace if we would only fully trust in God to direct our paths. We may not always understand what is going to happen, but what we do know is that, if we are part of the family of God, that it will happen exactly as God wants it to happen. We can have peace because our God is bigger than us and bigger than any situation we may find ourselves in.