OK, here's some of the main points Peter spoke of in that 2 Pet.3 chapter;
2 Peter 3:3-12
3 Knowing this first, that there shall come in the last days scoffers, walking after their own lusts,
4 And saying, "Where is the promise of His coming? for since the fathers fell asleep, all things continue as they were from the beginning of the creation."
5 For this they willingly are ignorant of, that by the word of God the heavens were of old, and the earth standing out of the water and in the water:
6 Whereby the world that then was, being overflowed with water, perished:
7 But the heavens and the earth, which are now, by the same word are kept in store, reserved unto fire against the day of judgment and perdition of ungodly men.
8 But, beloved, be not ignorant of this one thing, that one day is with the Lord as a thousand years, and a thousand years as one day.
9 The Lord is not slack concerning His promise, as some men count slackness; but is longsuffering to us-ward, not willing that any should perish, but that all should come to repentance.
10 But the day of the Lord will come as a thief in the night; in the which the heavens shall pass away with a great noise, and the elements shall melt with fervent heat, the earth also and the works that are therein shall be burned up.
11 Seeing then that all these things shall be dissolved, what manner of persons ought ye to be in all holy conversation and godliness,
12 Looking for and hasting unto the coming of the day of God, wherein the heavens being on fire shall be dissolved, and the elements shall melt with fervent heat?
KJV
Peter is talking about the fact of three world ages, with God already having destroyed one of them of old, and this present one we are in is to also be destroyed. And then God will in final institute a new heavens and a new earth for His Eternity.
But how do the scoffers see this world? They believe it will continue to exist as is, and that it has always been. They are willingly ignorant of how God destroyed the old world, and instead want to believe in their own permanence of things. Thus they don't see what's coming with the end of this present world either.
But because 'we'... (and those Peter was speaking to), do... know these things will come to pass as written in God's Word, what manner of persons ought we to be in all holy conversation and godliness?
This is a huge perspective Apostle Peter is offering us here. It is in a sense, showing our Heavenly Father's eternal Nature in relation to these three world ages, that they are just a drop in the bucket of time to Him. Likewise we should have this far-sighted view of His creation of the past old world, the present, and the one yet future, making our Faith on Him and His Son strong today while at the same time we know the things of today are going to end and we patiently wait for them.
This is also one of things Apostle Paul was speaking of in the Romans 8 chapter in regards to God's creation of world ages, specifically Rom.8:18-25, a Scripture that many have struggled with.