The head of state and other representatives are elected but they do not have uncontrolled power. What they may do is written in the constitution. If there is dispute about what the constitution means, this is decided by a court which is independent from the politicians.
The constitution describes how the state may be run. The constitution limits the power of each officeholder. Constitutional republics usually have a separation of powers. The separation of powers means that no single officeholder gets unlimited power. John Adams said that a constitutional republic was "a government of laws and not of people".
Constitutional governance argue is meant to be a safeguard against tyranny. No office holder can get to a position of absolute power. However, some have argued that a constitution can be written in such a way that it lets tyranny arise, and that a constitution is therefore not a fail proof safeguard against tyranny. 
Aristotle was the first to write about the idea in his works on politics.
Comparisons can be made. There are countries which nominally are constitutional republics, but which have become (in effect) dictatorships. There are also countries which have no written constitution, and are monarchies, but which act in a similar way to constitutional republics.
- Levinson, Sanford. 1989. Constitutional faith. Princeton University Press.
- Delattre, Edwin. 2002. Character and cops: ethics in policing, American Enterprise Institute, p. 16.