This paragraph is like a “last testament” for Peter. He knows he will be executed soon and he wants to encourage the readers to keep what he has said in mind even after he is gone. Some of the language here is “stock language” used in last testaments, both in the Bible and I the literature of the Second Temple period.
The prediction of Peter’s martyrdom at the end of John’s gospel generated a number of extra-biblical legends about
the kind of death Peter would experience, including a legend that Peter met the resurrected Jesus on the road to Rome and Jesus told him he was about to be 
In 2 Peter, he uses a vivid metaphor for death, he will soon be putting off the “tent of his body.” This phrase is usually associated with Bedouin who pack up their tent when they are ready to move on to a new location. Peter knows the time is near for him to leave be body and move on to what is next.
Since he knows he is about to die, Peter wants his readers to remember his personal testimony about Jesus. This would include his ethical teaching in the previous chapter he also is looking ahead to the personal testimony in the next few verses, that he was a witness to the transfiguration. For many of his readers, Peter will be a last connection to the life of Jesus. An eyewitness was respected more than a written source by many in the ancient world, so Peter wants his readers to remember what he is about to tell them in the next paragraph.
He wants to “stir up” his readers “by way of a reminder” (ESV). To “stir up” (διεγείρω) is a word used for rousing someone from sleep, to “awaken” a thought in the mind of the readers. The noun (ὑπόμνησις) is a reminder, so the meaning here is to awaken a particular thought. Think of this as a trigger for a flood of memories. Peter’s goal is to provide a trigger in the minds of his readers so they recall what he has taught them about Jesus and living an exemplary life. Alluding to the story of the transfiguration is part of that trigger.
Likewise, the phrase “make remembrance” (μνήμη, v. 15) refers to a memorial, a marker set up to remember someone or a special event. Some of my students create elaborate mnemonic devices to recall things for quizzes. I know this because they write random letters in the margins to help remember things, although sometimes remember the crazy word or sentence, but forget the thing they were supposed to remember in the first place! Peter’s words are to be like a memorial stone set up to remind people of the ethical teaching in the previous paragraph and the glorious revelation of Jesus in the following.
This “last testament” of Peter is a way of introducing the main goals of the rest of the letter. Peter wants his readers to recall his testimony about Jesus and his return in the face of opponents of the apostolic teaching about the return of Jesus.
culture. If you really cannot see well, you find yourself in difficult, embarrassing, or potentially dangerous situations. It is one thing to not be able to read a menu in a restaurant, for example, and quite another to not be able to tell one person from another. Worse yet, if you cannot see well enough to read street signs, driving a car becomes very dangerous.
said you would do, etc. Like blindness, forgetfulness can lead to embarrassment (who are you again?) but also to potential danger. Think of people who have serious problems remembering who they are, such as an amnesiac or a person suffering from Alzheimer syndrome. It might be dangerous for a person to be on their own because they have forgotten critically important information that will keep them out of danger.
Pursuit of virtue must be a strenuous effort on the part of the believer. “Make every effort” implies deliberate action. Someone might claim to be growing in godliness, but if there is no deliberate activity then the claim is empty. Imagine someone who claims to be trying to lose some weight, but they are not dieting or exercising. They are not really making “every effort” to lose weight! This is a bit like a “good faith effort” in modern English, but perhaps stronger. It means that the person really does make an honest effort to pursue virtue and godliness.
In some basic math classes a student is allowed to make a 3×5 card of information they might need to pass the test (basic formulas or methods for solving problems). Image a crafty student who prints out the entire math book in micro print and then brings a magnifying glass to class. He would be very prepared. Another student might just being a 3×5 card with nothing on it. But the most prepared student would be the one who had a card prepared by the professor with all the answers already on it.
Imagine contemporary celebrations like Mardi Gras, New Year’s Eve, or Super Bowl parties. There are all excuses for indulging in behavior that would be inappropriate at other times. But this goes beyond the pale: imagine someone behaving so badly at Mardi Gras that people thought they were crossing the line.