According to the author of the book of Nehemiah, this verse tells us that all the leaders from a special family called Levi were written down in a book to keep track of them for a long time. This was like keeping a list of important helpers for God's house so people would remember them.
Nehemiah 12:23: The sons of Levi, the chief of the fathers, [were] written in the book of the chronicles, even until the days of Johanan the son of Eliashib.
This verse advises avoiding genealogies, which contradicts Nehemiah 12:23's focus on genealogical records.
Titus 3:9: But avoid foolish questions, and genealogies, and contentions, and strivings about the law; for they are unprofitable and vain.