A monarchist is someone who believes their country should be ruled by a king or queen. The word does not tell you how much power they want that person to have. Some monarchists want the monarch to hold real power; many others are happy with a constitutional monarch who is a symbol while a parliament makes the laws. It is a politics word, a little formal. The opposite idea, in the older sense, is a republican: someone who wants a country with no king or queen at all (that is not the same as the US Republican Party). In history books you may also see royalist used in a close way, especially for people who fought for a king.