Yes, God does forgive us and cleanse us of all our sins when we trust Christ and commit our lives to Him. Some of the most reassuring words in all the Bible are these: "The blood of Jesus, his Son, purifies us from all sin" (1 John 1:7).
But we still have the capacity to sin—and the reason is because we are still sinners! You see, in the Bible there is a difference between "sin" and "sins." "Sins" are those things we do that are wrong—evil actions, wrong thoughts or motives, harsh or unkind words, even failing to do something we should have done (such as loving others). When we sin, we should confess it immediately and ask God for forgiveness.
But "sin" is something deeper. Sin is like a disease—a spiritual disease that resides deep within us all. And as long as we live, this disease of sin will still be part of us. Only in heaven will it be killed, and we will become like Christ. The Bible says, "But we know that when he appears, we shall be like him, for we shall see him as he is" (1 John 3:2).
Pause right now and thank God for forgiving you of all your sins. Thank Him too that He now lives within you by His Holy Spirit, and that each day He will help you overcome your old sinful nature as you submit your life to His control. Most of all, thank Him that someday our battle with sin will be over, and we will be with Christ in heaven forever.