"The life appeared, we have seen it and testify to it, and we proclaim to you the eternal life, which was with the Father and has appeared to us." NIV translation
He continues to remind us that Jesus was born, lived among men, and died. But, he also reminds us that Jesus was resurrected and, since He lives forever, we have that same hope. John doesn't just know of these things; he was there for most of them. He was the one that was with Jesus at the crucifixion as well as when he was gone from the tomb. He was also there when the resurrected Jesus appeared to them, taught them, and gave them the gift of the Holy Spirit. John is confident in what he has experienced and we can have that same confidence through the working of the Spirit.
"We proclaim to you what we have seen and heard, so that you also may have fellowship with us. And our fellowship is with the Father and his Son, Jesus Christ." NIV translation
John tells us why he shares the gospel of Jesus Christ and reminds us again that it is what he has actually seen and heard. He says that the reason is so that we may have fellowship together with God. The fellowship that he is talking about is not what it has come to mean in the "church" today. What John is talking about is believers in Jesus Christ meeting together to share the things of Christ.
It is not getting together for food and talking about sports, news, or the latest trends. It is sharing what God is doing in our lives and the purpose is to build each other up in the faith. A good example of this is described in Acts 2:42-47. Remember that John would have been a part of the fellowship described in that passage because he was there in Jerusalem at the time.
"We write this to make our joy complete." NIV translation
Some manuscripts have "your" in place of "our" but either way joy comes from the Lord and a proper relationship with God. John's purpose in this letter is to remind people of that relationship and how to put our faith into action.
"This is the message we have heard from him and declare to you: God is light; in him there is no darkness at all. If we claim to have fellowship with him yet walk in the darkness, we lie and do not live by the truth. But if we walk in the light, as he is in the light, we have fellowship with one another, and the blood of Jesus, his Son, purifies us from all sin." NIV translation
Light and darkness just do not go together for, as soon as light appears, darkness disappears. Likewise, if we are saved by the blood of Jesus Christ, our actions change and we are a new creation. This new creation has fellowship with God and that relationship with God allows us to have fellowship with one another.