1 Nephi 6

About 10 years after they left Jerusalem, Nephi was commanded to make large plates and engrave or write a history of their journeys and their family. About 20 years after that, he was commanded to make small plates and on those write a history of the more sacred things that took place and were taught. We are reading what he wrote on the small plates. The small plates start with 1 Nephi and continue until we get to Mosiah and then they end. So we are reading what Nephi began writing about 30 years after they left Jerusalem. It helps to remember that when Nephi says "these plates," he's talking about the small plates.

The small plates were fewer in number and smaller in size. This is why Nephi says he doesn't have room talk about everything that happened to his father and the family. With so little room, he only wants to write the things of God so he can persuade people to come unto Christ. I think verse 5 is the key verse where he says he is not going to write anything that would be pleasing to the world. He's not concerned about what the world will think and knows that those caught up in the world will not be able to understand it. He only wants to write what will please God.

There are two good verses to cross reference with verse 5. In 2 Nephi 25:23, Nephi says, "For labor diligently to write, to persuade our children, and also our brethren, to believe in Christ, and to be reconciled to God; for we know that it is by grace that we are saved, after all we can do.
2 Nephi 33 contains the last words he wrote on the small plates. Verse 10 says, "And now, my beloved brethren, and also Jew, and all ye ends of the earth, hearken unto these words (what he has written on the small plates) and believe in Christ; and if ye believe not in these words believe in Christ. And if ye believe in Christ ye will believe these words, for they are the words of Christ, and he hath given them unto me; and they teach all men that they should do good." Notice how many times he pleads with us to believe. He is someone who knows, who has seen the Savior, and has given his life to teach others the truth concerning the Savior. You might want to read the last five verses of 2 Nephi that come after that.