"But if anyone obeys his word, God's love is truly made complete in him. This is how we know we are in him: Whoever claims to live in him must walk as Jesus did." NIV translation
John is simply saying that we have to walk the talk. Imitating someone is the highest form of flattery and praise as many people try to dress and act like sports stars or actors. A good part of the economy is based on the fact that people have to buy the latest thing to be like the "stars". It is the same principle here in that, if Jesus means that much to us and we respect Him as much as we say, then we will try to imitate Him in all of our ways. We do not walk to be saved (we bow in prayer) but we honor and glorify through our walk (being transformed to be like Jesus). This walk is a natural reaction to love for the Savior when we understand what He did for us!
"Dear friends, I am not writing you a new command but an old one, which you have had since the beginning. This old command is the message you have heard. Yet I am writing you a new command; its truth is seen in him and you, because the darkness is passing and the true light is already shining." NIV translation
Although this passage may seem confusing, John is simply trying to get the believers to remember their calling. It is not a new command as Jesus called us to love our neighbor as ourselves. It is a new command in that they have not followed it from the beginning as they should.
"Anyone who claims to be in the light but hates his brother is still in the darkness." NIV translation
John continues to use the contrast between light and darkness and with good reason. God is light and we are told that, in the new heaven and the new earth, God will be the only light as there will be no need for a sun, moon, or stars (see Revelation 21:23). Light and darkness do not mix because, as soon as any light appears, there is no more complete darkness. In the same way, love and hate do not mix. All men are created in God's image (see Genesis 1:27). Therefore, we cannot hate men and love God.
"Whoever loves his brother lives in the light, and there is nothing in him to make him stumble. But whoever hates his brother is in the darkness and walks around in the darkness; he does not know where he is going, because the darkness has blinded him." NIV translation
Did you know that your hate toward someone can affect you more than them? That is what John is saying here in that, when you hate someone, it causes you to stumble in your walk with the Lord. Hate is disobedience to God and disobedience brings separation. The further we get away from God and His will for our lives the less light there is shining in our life and therefore more darkness which is simply an absence of light. If you walk long around enough in the dark, you are going to end up headed in the wrong direction. We can easily get headed in the wrong direction and be walking away from the light that is God but He is always there waiting for us to stop and turn back towards Him (repent) and He will lead us back to Himself.