The first nine chapters are composed of long, detailed genealogies. These occasionally diverge from our understanding of things as detailed in earlier Books, including the Torah itself! This is not as troubling as some readers might find it. First off, many discrepancies can be immediately dismissed by recognizing that numerous people throughout the Biblical era were known by multiple names; Jacob was also called Israel, Hadassah was called Esther, etc. If one is incredulous that Saul's grandfather Aviel was called "Ner" (lamp) because he lit the street lamps, try explaining to someone 2,000 years from now why Arnold Schwarzenegger is called "The Governator."
And what about large omissions in the text? These chapters were compiled by Ezra, from the genealogies kept by the Tribes. Some Tribes did a better job retaining their family histories; others, not so much. Ezra recorded what the Tribes had provided, leaving out what was missing. (Some Tribes are absent altogether!)
But why should something as mundane as family records be canonized into the Bible? Again, this is not unprecedented. Numbers 21:14, for example, quotes from the no-longer-extant "Book of the Wars of G-d," while a letter written by Nebuchadnezzar occupies more than an entire chapter of Daniel. Quoting a book in the Bible is no more inherently surprising than quoting the conversation of Pharaoh or Balaam; their words may not have been holy when they uttered them, but they are now bona fide Biblical verses.
The rest of the Book is historical narrative, but its focus is different than that of Judges, Samuel and Kings. The focal point here is on the Davidic dynasty, with the result that the narrative begins just prior to David's ascension to the throne. Incidents from the Books of the Early Prophets may be told from another perspective, or omitted altogether, while some stories may be recorded here for the first time. (One noteworthy incident is the murder of Zechariah the priest in II Chronicles 24, which has no parallel account in the Book of Kings.)
One final note: the commentary popularly attributed to Rashi is generally accepted to be by other hands. This is the case in several Biblical Books and the author is often referred to as "Pseudo-Rashi." Here, we have taken to referring to this commentary as that of "Rashi" (with the quotes).