Short answers, pulled from the story.
Signals intelligence, or SIGINT, is the collection and analysis of information gathered by intercepting signals. Its two main branches are communications intelligence (COMINT), which covers signals between people, and electronic intelligence (ELINT), which covers electronic emissions not directly used in communication, such as radar.
Electronic interceptions appeared as early as 1900, during the Boer War of 1899-1902. The birth of modern signals intelligence is dated to the Russo-Japanese War of 1904-1905, when the British ship HMS Diana intercepted Russian naval wireless signals in the Suez Canal, the first such interception in history.
Room 40 was the Admiralty's interception and decryption service, established by Sir Alfred Ewing at the direction of Rear Admiral Henry Oliver. It intercepted virtually all official German messages and decrypted over 80 million words of German wireless traffic over the course of the war, including the Zimmermann Telegram sent to German ambassador Heinrich von Eckardt in Mexico.
Ultra was the code name for all British SIGINT and codebreaking operations in World War II, managed from Bletchley Park. Dwight D. Eisenhower described it as having been decisive to Allied victory. Historian Sir Harry Hinsley argued that Ultra shortened the war by not less than two years and probably by four.
Traffic analysis was used both offensively and as a tool for deception. As part of Operation Quicksilver, Allied radio transmissions simulated the headquarters of the fictitious First United States Army Group, commanded by George S. Patton, to mislead German defenders about the true Normandy landing site. Japan used the same technique before Pearl Harbor, broadcasting false signals from carriers in home waters while the attacking fleet moved under radio silence.
GC&CS was Britain's first peacetime codebreaking agency, officially formed on the 1st of November 1919. Its public mandate was to advise government departments on cipher security; its secret directive was to study foreign cryptosystems. By 1940 it was working on the diplomatic codes of 26 countries and tackling over 150 cryptosystems.