Short answers, pulled from the story.
The Jacobin Club was the most influential political club during the French Revolution of 1789. It originated as the Club Breton, a group of deputies from Brittany attending the Estates General in May-June 1789, and was formally re-founded in November 1789 in Paris, where it took the name Jacobins from the Dominican monastery on the Rue Saint-Honoré where it met.
At its height, the Jacobin Club had a nationwide membership estimated at half a million or more, organized across at least 7,000 affiliated chapters throughout France. The Paris society alone was composed largely of professional men and well-off bourgeoisie, as the subscription fee excluded most working people.
The Reign of Terror refers roughly to the period from June 1793 to July 1794, when the Mountain faction led by Maximilien Robespierre controlled the French government through the Committee of Public Safety. During this period, 17,000 death sentences were carried out nationwide and well over 10,000 people were put on trial and executed, many for political crimes.
Robespierre was a lawyer from Artois who became the dominant voice in the Jacobin Club by September 1792 and entered the Committee of Public Safety in July 1793. He earned the nickname l'Incorruptible for his refusal to compromise his principles, and was ultimately sentenced to death and guillotined on the 28th of July 1794, along with 21 associates.
The National Convention permanently closed the Jacobin Club on the 22nd of Brumaire, which was the 12th of November 1794, by a nearly unanimous vote and without debate. The closure followed the Thermidorian Reaction after Robespierre's execution, attacks by anti-Jacobin gangs called the jeunesse dorée, financial disarray, and falling membership.
In modern France, Jacobin generally denotes support for equal formal rights, centralization of government, and a strong role for the state in shaping society, particularly through a state education system that promotes civic values. It is sometimes used as a self-identification by proponents of a strong nation-state and is distinct from the terror associations the word carried in the 19th century.