Short answers, pulled from the story.
The alliance emerged in 60 BC as a secret understanding to use mutual influence to bypass constitutional vetoes. Plutarch places the alliance before Caesar's election while Cassius Dio suggests it formed afterward. A letter from Caesar to Cicero dated December 60 BC implies the pact was still being negotiated at that time.
Gnaeus Pompeius Magnus, Marcus Licinius Crassus, and Gaius Julius Caesar formed the alliance in 60 BC. Each man possessed enough influence to cause chaos but lacked the collective power to force through their specific goals against a gridlocked Senate. The alliance included support for allies like Lucius Afranius and Lucius Flavius during its early stages.
Crassus launched his invasion of Syria in early 53 BC and suffered a catastrophic defeat at the Battle of Carrhae months later. He and much of his army were killed by the Parthians which marked the conversion of a balanced three-person alliance into a dyadic rivalry between Caesar and Pompey. This disaster shattered the balance of power within the group.
The term appears nowhere in any ancient source and refers to no official position held by Caesar, Pompey and Crassus. Cicero contemporaneously wrote of three men exercising regnum while Marcus Terentius Varro called it a three-headed monster. Modern scholars regularly avoid the term because it is misleading when equating the position of the 50s with the official triumvirate of Antony, Lepidus, and Octavian.
Usage of the term emerged only during the 18th century and was first attested in 1681. Knowledge that the term was a modern coinage remained unknown until revealed in 1807. By the 19th century usage became regular mostly in English and French sources.