The Reign of Terror was a period during the French Revolution when the government used terror tactics to force all citizens of France to show loyalty to the French Republic, which had been established in 1792. The Committee of Public Safety led the government, headed by Maximilien Robespierre. The Committee of Public Safety imposed "The Terror" in 1793-94, a program which intimidated citizens into loyalty by punishing any instances of suspected disloyalty. An enormous number of citizens were executed by guillotine for failing to show full support of the Revolution's goals.
As for how this damaged the ideals of the Enlightenment, let's back up and consider what the ideas of Enlightenment political thought were. Enlightenment thinkers promoted the rights of citizens and the people's authority to create--and to change--their own governments. The French Revolution motto of "Liberty, Equality, Fraternity" embodied Enlightenment political ideas.
The old order (or ancien regime), prior to the Revolution, had demanded loyalty to an absolute monarchy. In ending that political model and creating a new republic based on the rights of individuals as citizens, the hope was that greater liberty and fraternity would exist in the nation. However, the new order found it necessary to enforce loyalty to the Republic and its ideas. That is what prompted the "Reign of Terror." So the new order became as radically absolute in its loyalty demands as the old order had been in its traditional expectations. In that way the Enlightenment ideas were shown to be vulnerable to the same flaws as previous ideas had been. When a king was in charge, there could be abuse of political power. When the people took charge of the nation for themselves, there could also be abuse of political power.
