A constitutional republic is a state in which the head of state and other officials are representatives of the people and must govern according to existing constitutional law that limits the government's power over all of its citizens. Because the head of the state is elected, it is a republic and not a monarchy.
In a constitutional republic, executive, legislative, and judicial powers can be separated into distinct branches.
The fact that a constitution exists that limits the government's power makes the state constitutional. That the head(s) of state and other officials are chosen by election, rather than inheriting their positions, and that their decisions are subject to judicial review makes the state a republic.
John Adams defined a republic as "a government of laws, and not of men." Constitutional republics attempt to weaken the threat of majoritarianism and protect dissenting individuals and minority groups from the "tyranny of the majority" by placing checks on the power of the majority of the population. The power of the majority of the people is limited to electing representatives who legislate within the limits of an overarching constitutional law that a simple majority cannot modify.