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 crucified (Acts of Peter). There is nothing historical in these stories since the point of Jesus’ prediction was only to tell Peter that his faith was not weak and that he would persevere all the way to the end.
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.