When you state a fact or opinion confidently, and then say it again with equal force, you reassert it. You can also reassert forceful behavior, like when a teacher reasserts control over a rowdy classroom.
You might reassert your belief that one presidential candidate is much better than another, or reassert your innocence when a question of someone stealing cookies from your grandparents' cookie jar is raised more than once. You can also reassert authority, the way a librarian does, hushing a conversation that's become too loud and boisterous again. Reassert adds the "again" prefix re- to assert, from the Latin asserere, "claim, maintain, or affirm."