[notdonspaulding]

This (the USA, at least) is a constitutional republic. You have representation and you have constitutional rights. In a democracy, a plurality of the people can vote to do whatever they want to you. In a constitutional republic, a supermajority has to change the nature of your rights in order to violate them.

It's an important distinction.

[Kalium]

The USA is a symmetric federalist constitutional republican representative democracy. This is a form of democracy.

"Democracy" is a family of types of government, of which the absolute democracy many imagine in one form. A representative democracy is another.

[everybodyknows]

A colorful illustration of the value of such checks on power would be the incident in which a single majority vote in the legislature of imperial Athens sufficed to send off a galley to their rebellious colony of Mytilene, with orders to put every male inhabitant to the sword.

As it happened, the next day the assembly changed its mind, and sent off another galley rescinding the order. The second galley was indeed able to overtake the first in time. Thucydides attributed this to deliberate slowness by the captain of the first.