A good short biography of Jacob is available at the Encyclopedia of Mormonism here.
Jacob starts out by explaining that 55 years "had passed away from the time that Lehi left Jerusalem." Jacob was born in the wilderness, so he never saw Jerusalem. We don't know when Nephi was born, but we can estimate he was around 15 when Lehi left Jerusalem, making him about 70 years old when he gave the plates to Jacob. Jacob was born a few years after they left Jerusalem, say 5 years. That would make Jacob 50 years old when he started this record.
Like all but one book in the Book of Mormon, the book of Jacob is named after the main character--the person whose book it is. (The exception is Mosiah, which starts with King Benjamin as the main character. What we know as Mosiah chapter 1 was originally chapter 3, but Martin Harris lost the first two chapters as part of the lost manuscript. We know from Omni that King Benjamin's father, Mosiah, was an especially important figure because he led his people to find the land of Zarahemla, so probably the first two chapters of Mosiah that were lost discussed that King Mosiah. See Omni 1:23.)
Jacob makes two fascinating points in Jacob 1. First, he says Nephi "anointed a man to be a king and a rule over his people." Jacob doesn't even identify the man. I infer this means the king was not a descendant of Nephi and probably not even a descendant of Lehi.
Some commentators think the new king--"Second Nephi"--was Sam, or Sam's son. E.g., see here. Others think Second Nephi was probably one of Nephi's sons. See here.
These assumptions seem premised on two things: the pattern in the Bible (kings naming sons as successors), and the assumption that Nephi's people consisted of Lehi's family, plus Zoram. As I've explained before, I think when Lehi's family landed in Florida, they encountered indigenous hunter/gatherer people whom they taught and converted. Some of the indigenous people joined with Laman, while others went with Nephi to settle the land of Nephi (in Tennessee). For whatever reason, Nephi named one of these people as his successor. Perhaps he wanted to help unite the people, or maybe one of his daughters married one of the indigenous men. (BTW, I also think the indigenous people they encountered were descendants of Jaredites, but we'll discuss that when we get to Ether later this year.)
In this scenario, it makes sense that Jacob would identify Second Nephi as simply "a man." And it also makes sense that Nephi would entrust the plates to his brother to keep them in the family line.
Another consideration is Jacob's criticism of the new king in verse 15. It's possible Jacob did not identify the king because he disapproved of him; i.e., he would not want to blame one of his nephews for the wicked practices that arose under the reign of the second king. However, Jacob seems to distance himself (and his brother Joseph) from the new king, essentially ignoring him and speaking directly to the people.
The second fascinating point is in verse 13:
13 Now the people which were not Lamanites were Nephites; nevertheless, they were called Nephites, Jacobites, Josephites, Zoramites, Lamanites, Lemuelites, and Ishmaelites.
14 But I, Jacob, shall not hereafter distinguish them by these names, but I shall call them Lamanites that seek to destroy the people of Nephi, and those who are friendly to Nephi I shall call Nephites, or the people of Nephi, according to the reigns of the kings.
This reinforces the idea that indigenous hunter/gatherers were aligning themselves to the family groups who came with Lehi. It's possible these tribes merely reflect the descendants of the men after whom they are named, but that seems unlikely given the description of wars among the people. Plus, Jacob doesn't use genetics to distinguish the groups. Lamanites are those "that seek to destroy the people of Nephi," while Nephites are "those who are friendly to Nephi." That description is exactly what we would expect if people are aligning themselves based on ideology or preference instead of genetics.
One last point. Jacob accuses the people of searching "for gold and for silver and for all manner of precious ores." This is another indication of a North American setting.
From Moroni's America: Jacob doesn’t offer much in the way of geographical information, but he does demonstrate familiarity with the Lamanites in Jacob 3:5-9. (In fact, he seems to be denouncing the Nephites’ animosity toward the Lamanites, including racism and cultural denigration, as much as the other sins he accuses the Nephites of committing.)[i] This familiarity suggests the two groups were in close contact. Despite their differences, the Nephites and Lamanites were surely trading with each other.