How the Terror started is a question we can definitely answer. Why it happened is a lot more difficult, and we may never quite know for sure; but we can at least make some educated guesses. In 1793, France was in a state of chaos--a bitter and bloody civil war...
How the Terror started is a question we can definitely answer. Why it happened is a lot more difficult, and we may never quite know for sure; but we can at least make some educated guesses.
In 1793, France was in a state of chaos--a bitter and bloody civil war after the start of the French Revolution that had splintered into multiple revolutionary and counter-revolutionary factions. On August 6, the Comite de Salut Public (Committee for Public Safety), led by Maximilien Robespierre, took control and became the de facto government of France (though they never officially considered themselves a government).
Robespierre had two primary goals, which seemed reasonable enough: Restore order, and establish a free Republic of France. But in order to achieve those goals, he was prepared to use any means necessary--and that's where the Terror comes in.
Initially, the Terror was just the executions of King Louis XVI and Queen Marie Antoinette, along with a few dozen leaders of the Girondists, a rival revolutionary faction that was more friendly to the monarchy and supported war with other countries in Europe. These weren't exactly fair trials, but had they been fair trials, most of those leaders probably would have been legitimately convicted of treason and executed.
But this was not enough to restore order, and the Comite escalated from there. They began executing people for even minor involvement in counter-revolutionary activities, and then for simply expressing counter-revolutionary opinions, and ultimately for petty crimes or no apparent reason at all. In all some 30,000 people were killed. Robespierre believed that the power of government came from its ability to terrify people, and so he actively sought to inspire fear in the population by ruling with an iron fist.
Why did all this happen? I attribute it mainly to two factors:
First, Robespierre's very all-in, no-holds-barred, "the ends justify the means" approach, where he was willing to do just about anything as long as he thought it would help establish the Republic of France. He thought that killing thousands and terrorizing millions would help, so he ordered it done.
Second, the extreme anger felt by the revolutionaries against the monarchy and all who had supported it. Much of this anger was quite justified---the monarchy in France had been quite oppressive at times, and wealth inequality in France before the Revolution was astonishingly, horrifically huge. But anger is one of the strongest, most basic emotions, and it has a way of getting out of control very easily. The legitimate executions of a few actual monarchist leaders spiraled out into beheading of anyone who seemed to vaguely resemble an enemy of the Republic.