"So I will always remind you of these things, even though you know them and are firmly established in the truth you now have." NIV translation
There is much in the Word of God and, even though we may have a firm grasp on our faith, we still should study the entire Word of God to keep it fresh in our minds. Just as Peter said here, we hope to remind you of parts that you may not have studied for awhile.
"I think it is right to refresh your memory as long as I live in the tent of this body, because I know that I will soon put it aside, as our Lord Jesus Christ has made clear to me." NIV translation
Peter knew that he was going to die for his faith and that it was going to be before Jesus came back to get the church. That is why he did not spend much time telling of that day.
"And I will make every effort to see that after my departure you will always be able to remember these things." NIV translation
He spent his time helping others (including us) to realize what we have in Christ. He consistently preached the same message of hope and through repetition as well as example the people of that day were able to remember. Peter must have also had someone write these letters and preserve them and they have been passed on to us even today.
"We did not follow cleverly invented stories when we told you about the power and coming of our Lord Jesus Christ, but we were eyewitnesses of his majesty." NIV translation
Peter is talking about the resurrection of Jesus Christ and the fact that he was a witness of what happened. The cleverly invented stories that he is talking about is that the religious leaders got together and made up the story that Jesus' body was stolen (see Matthew 28:11-15).
"For he received honor and glory from God the Father when the voice came to him from the Majestic Glory, saying, 'This is my Son, whom I love; with him I am well pleased." NIV translation
This is the message that God gave when Jesus was baptized (Luke 3:21-22) as well as when he was transfigured (Matthew 17:5). He was declared to be the Son of God and the belief in that fact is how we can tell whether a message is from God or from the devil. (see 1 John 4).