To reunite is to come together again, or to bring people or parts together again. Families reunite after a long trip. A band that broke up years ago may reunite for a concert. You can also reunite the parts of a group, a political party, or a country, so this word is wider than reunify. It can happen by itself (“they reunited”) or because someone makes it happen (“the show reunited the old team”). It is common and not especially formal. Though actually, for a split country in history-book English, reunify / reunification often sound more exact — but reunite is still used there too.