When you say something again, you restate it. If you give a speech, you might decide to express your main idea at the beginning and then restate it a second time, near the end.
Often when you restate something, you say it in a slightly different, perhaps clearer way, with the intention of really getting your point across. A teacher might sweetly ask her class to come in from recess, and then restate her request five minutes later by saying, "If you aren't inside when I count to 30, there will be no recess tomorrow!" The verb restate combines the prefix re-, "again" in Latin, and state.