Whether states can ban AR-15 style firearms may now reach the Supreme Court, the court that has final say on what the Constitution permits. The federal government has expressed support for a legal challenge to those bans. A challenge, in legal terms, is a lawsuit or appeal arguing that a law is unconstitutional.
The position puts the executive branch on the side of those seeking to overturn the bans. The Supreme Court controls its own docket, taking only a fraction of the cases brought before it each term, and institutional backing from the federal government can factor into whether the justices agree to hear a case at all.
AR-15 style firearms are a category of semi-automatic rifle. Semi-automatic means the weapon fires one round per trigger pull. Several governments have moved to ban or restrict them, and those prohibitions are at the center of the dispute the federal government has now stepped in to support.