"I write to you, dear children, because your sins have been forgiven on account of his name." NIV translation
John begins to explain to the readers of this letter the reasons for his writing it. The first is addressed to all believers (dear children) and he is saying that he is writing it because, as believers, we are called to put our faith into action (walk the talk).
"I write to you, fathers, because you have known him who is from the beginning. I write to you, young men, because you have overcome the evil one. I write to you, dear children, because you have known the Father." NIV translation
Now, John touches on three age groups (children, young men, and fathers) but he says for all of them it comes down to the fact that they know God and have overcome sin through Jesus Christ. It also sort of reminds us of the stages in our faith as we simply start out believing in God and salvation through Jesus Christ (we become children). Then, we contend in that faith as we struggle with the "evil one" (we grow and mature in our faith to be young men). Finally, as fathers, we pass the faith on to our children and it is simply back to believing in God and salvation through Jesus Christ.
"I write to you, fathers, because you have known him who is from the beginning. I write to you, young men, because you are strong, and the word of God lives in you, and you have overcome the evil one." NIV translation
John has basically repeated the same thing in this verse as he did in verse 13. The significance is that, when things are done twice, it reminds us that the number two is the number for witnessing throughout the Bible.
"Do not love the world or anything in the world. If anyone loves the world, the love of the Father is not in him." NIV translation
This verse may be a little confusing at first but, when you understand what John means by the "world", it makes sense. When he talks of "the world", he is not talking about the things that God has created. If you look back to Genesis 1, when God created the earth, He said it was good and He said that man was created in His image. Therefore, what John is talking about is the system of this world and the effects of sin. When sin came, everything that was created was affected by the presence of what was not good. Everything was diminished and is less than the perfect that God had created (but He is going to restore all things). We are to long for the best that God has and not love the diminished things that we see now. The second thing John means by "the world" is the system of the world as it too is less than the perfect that God intended. We now have governments and authorities other than God and that was not what creation was designed for. When everything is made new, the only authority and system will be God himself living with us just as it was in the Garden of Eden. John is also saying that you have to make a choice because you cannot love the diminished things (they are less than perfect) and love God (who is perfect).