A monarchy is when a King (and now) Queen rules over a country because they are royalty (born or married into it). They make the decisions for their country that they think will help.
A oligarchy is when a few people rule over the rest and make the decisions for the rest.
A dictatorship is when one person rules over the rest, who don't have a say in how the country is run or who is in government. Many bad things have come out of dictatorships in the past, e.g Kim Jong Un, Adolf Hitler and the concentration camps.
A democracy is when everyone over a certain age gets a vote on who gets into the government. Until recently women haven't been allowed to vote, and still aren't in some countries!
A theocracy is when the government is a ruled by a priest in the name of god/gods. This doesn't happen very often anymore but it often happened in the bible or the ancient Romans.
An anarchy is when no one rules. This often happens in times of war or when war has just finished.