According to the author of the Chronicles, this verse tells us that after Jeroboam had been king for 18 years, a new king named Abijah started to rule over a place called Judah. It shows how leaders change, and people were paying attention to when new kings began their rule.
2 Chronicles 13:1: Now in the eighteenth year of king Jeroboam began Abijah to reign over Judah.
States that Abijam became king of Judah in the eighteenth year of Jeroboam's reign, which may create confusion regarding the timeline of Abijah's reign mentioned in 2 Chronicles 13:1.
1 Kings 15:1: Now in the eighteenth year of king Jeroboam the son of Nebat reigned Abijam over Judah.