Short answers, pulled from the story.
The Thermidorian Reaction was the period between the ousting of Maximilien Robespierre on 9 Thermidor Year II (the 27th of July 1794) and the inauguration of the French Directory on the 2nd of November 1795. It marked the end of the Reign of Terror, a shift away from radical Jacobin policies, and decentralization of executive power from the Committee of Public Safety.
Members of the National Convention, led by Jean-Lambert Tallien and Jacques Nicolas Billaud-Varenne, denounced Robespierre as a tyrant on the floor of the Convention on 9 Thermidor (the 27th of July 1794). He was declared an outlaw along with his followers, meaning he could be executed within 24 hours without trial. He was captured at the Hotel de Ville in the early hours of the 28th of July and executed that same day.
The White Terror was a period of violent repression against Jacobins, sans-culottes, and anyone associated with the radical left, carried out in part by a group called the Muscadin. In May and June 1795 it was especially intense, resulting in numerous imprisonments, prison massacres, and several hundred executions almost exclusively of people on the political left.
The Reign of Terror killed over 40,000 people. The White Terror of 1795 resulted in several hundred executions, considerably fewer, though many took place without a trial.
The Constitution of the Year III was drawn up on the 22nd of August 1795. It pulled back some of the democratic provisions of the 1793 constitution, establishing an electoral college for choosing officials and a bicameral legislature, with provisions designed to protect the current holders of power.
Napoleon Bonaparte commanded the troops that suppressed a royalist revolt on the 5th of October 1795 (13 Vendémiaire), crushing it with what became famous as "a whiff of grapeshot." This was one of his first prominent appearances in French political life, occurring just weeks before the Convention dissolved and the Directory took power on the 2nd of November 1795.