I'll deal with the interpretive issue first. Verse 6 says, "Everyone who resides in him [Jesus] does not sin; everyone who sins has neither seen him nor known him." Yikes. From an interpretive standpoint, this gets even more complex because at the beginning of I John 2, the author makes very clear that Christians do sin. I'm going to be honest and tell you that I'm not quite sure what to make of this passage. My best educated guess is that it is referring to "living a life of sin"--that is, living a life in which committing sin is the norm and there is no guilt for it. Here is a much better analysis of I John 3:6.
If this interpretation is correct, it still leads to a very difficult application. I grew up in a church that essentially taught what is sometimes referred to as "easy believism". Too often I hear something to the effect of, "If you ask Jesus into your heart, then you will go to heaven. It doesn't matter what happens from here on out, you can be sure of your salvation." Or, to put it differently, "Pray a prayer and you get your guaranteed ticket." (For the record, my church would have never actually stated the second version, but I have heard a more blunt pastor put it that way once.) The problem is that I don't see any way for this theological position to square with today's passage or many other places in the Bible. To read a much more thorough (yet still incomplete) analysis, check out John MacArthur's controversial The Gospel According to Jesus: What Is Authentic Faith?
This is a very dense chapter, but I want to bring out one final point. (I have a feeling this post will be edited and added to quite a bit in the future.) At the end of the chapter John summarizes what it means to be righteous before God. He says, "Now this is his commandment: that we believe in the name of his Son Jesus Christ and love one another, just as he gave us the commandment." My analysis of what "believe" means in the New Testament will have to wait for another day. But, righteousness is summarized as having true faith in Christ and loving each other. Very simple, but also very hard.