If there's one thing you know about America, it's that it is - despite all of its many flaws - a representative, federal, republican (with a small R) democracy. The "democracy" part means "rule by the people" - from the Greek demos, meaning people, plus kratos meaning rule.
That means the people are the supreme source of legislative power, as opposed to say, a monarch. The "representative" part means that the people elect representatives to represent their wishes and also their interests, the latter being especially important because sometimes the people do not have all the information and need experts to decide for us, for example about how to organize air traffic control or ban a given chemical.
This is as opposed to a direct democracy where all decisions are made collectively, through referendums or other methods. The "federal" part means that legislative power is diffused between the federal government and the governments of the 50 states. This is as opposed to one centralized authority.
The "republican" part means that America is a republic: that is, it belongs to the people, not to a ruler, and positions within its hierarchies are not inherited or bestowed by an unelected body. Living up to these ideals and the bedrock on which they rest - the rule of law, one-person-one-vote, equality before the law, etc. - is the work of generations.
Still, America is only one country, and there are 196 of them on the planet right now. Some are constitutional monarchies, others are absolute monarchies, some are federalized, others are centralized, some are ostensibly communist (though none is actually in practice) and some are failed states. Now we've covered some of the key terms describing them, let's see if you know which of these and others apply to which country!