The books of First and Second Kings are two of the historical books in the Old Testament. Originally they were a single book (and still are in the Hebrew Bible). Historically, the book of First Kings picks up where Second Samuel ends. The book of Second Chronicles is a parallel account of First and Second Kings, with a focus on the nation of Judah.
First Kings begins with the reign of king Solomon, David’s son and successor (First Kings 1 through 11). Solomon’s son, Rehoboam, succeeds his father as king, but following the bad advice of his peers, the nation is ultimately split in two. The larger part (10 tribes) picks their own king and continues to be known as Israel. The smaller part (the tribes of Judah and Benjamin) are ruled by Rehoboam and his heirs (who are king David’s descendents); it is called Judah.
After this division, the nation of Israel is ruled by evil kings and the people, for the most part, turn their back on God. As a result of their turning from God, the nation of Israel is eventually conquered and it’s people dispersed. The nation of Judah is ruled exclusively by descendants of king David, some of who are good and godly rulers, other are not. Later on, they are likewise conquered and all but the poorest people are deported to Babylon.
Most of the prophets lived during the timeframe covered in First and Second Kings. Their ministries and messages give additional insight into the reoccurring propensity of the nations of Israel and Judah to turn their backs on God.