This is where things really start to change in the Book of Mormon. Up to this point, the Nephites had been ruled by kings, but that was about to be thrown out the window. You see, after his sons repented, King Mosiah asked his people which of his sons they wanted to be king (just as a reference, their names were Ammon, Aaron, Omni, and Himner), and the people chose Aaron. See, the thing is, Aaron didn't want to be a king. In fact, none of them wanted to be king. They all felt so awful about what they had been doing they decided to go on a mission... to the Lamanites.
Mosiah was obviously terrified for his sons' lives. These were the people that had been trying to eradicate the Nephites since they got off Nephi's boat! So he prayed, and God promised him that, so long as he was faithful, his sons would not be harmed. With this in mind, Mosiah went to the people and explained what his sons had decided. When they wanted him to make one of his sons be king, he set down a few truths: 1) Being a king is freakin' hard! You have to be responsible for everyone in your kingdom, and if someone doesn't want that responsibility, the people have no right to force it on them. 2) As a king is responsible for everyone in his kingdom, it places an unfair amount of blame on him if the people turn wicked, because 3) 9 times out of ten, if the people are wicked, it's because the king has been giving a poor example. Mosiah proposed that he could remain king until he died, but when he did, the people should start electing their rulers. That way it was their fault if they elected someone wicked, and no one who didn't want to rule would be forced into that position. The Nephites loved the idea, and Mosiah became one of their most celebrated historical figures.
And so the Book of Mosiah ends, with Alma II becoming the first ever high judge (leader of the country) after Mosiah's death, and the four Nephite princes disappearing into the lands of the Lamanites.
Fare thee well, friend!