A more thorough explanation:

Definition: Maius Latium refers to the greater rights granted to the inhabitants of Latium and colonies outside Italy under Roman law. These rights included granting citizenship to all members of the local curia or town council and their children.

Example: Under the Principate, there were two types of Latium: Latium maius and Latium minus. Latium maius referred to the rights granted to colonies founded as a coloniae Latinae outside Italy, combined with the concession of Roman citizenship to a larger group of individuals than Latium minus. In Latium minus, only the municipal magistrates and members of the municipal council were rewarded with Roman citizenship.

This means that if you were a member of the local council in a colony outside Italy, you and your children would be granted Roman citizenship under Latium maius. However, if you were only a municipal magistrate or council member in a different type of colony, you would only receive citizenship under Latium minus.