I hope you like names, because we will be reading the names of Jews for the next week or so. The last chapter basically covered Adam to Abraham, Isaac, Jacob and Esau. This chapter covers from Jacob (Israel) to David with a few family offshoots covered as well. Really, this seems to be aimed at listing mostly the descendants of Jacob's son, Judah.
Judah did have some famous... and some infamous... sons. Er, Onan and Achan (I Chronicles 2:7) were certainly not descendants to be proud of. However, Hur, Caleb, Boaz, David, Abishai, Joab, Asahel and Amasa most certainly are names to be conveniently dropped into a conversation.
These genealogies must have had great significance in the decades immediately after they were recorded. For example, when the remnant of the Jews came back to Jerusalem in the days of Ezra and Nehemiah to rebuild the walls and the temple, these inspired genealogies and others (though not inspired of God) would surely have been invaluable in reestablishing families in their rightful places.
In our day, these genealogies probably function mostly in increasing our curiosity. For example, what do you make of the ''families of scribes" mentioned in I Chronicles 2:55? Perhaps they were the writers of parts of the Chronicles?