Unlike the first triumvirate, this was an official institution. In 43 BC, Octavian, Marcus Antonius and Lepidus were named triumviri republicae constituendae (the triumvirate to administer the Republic) and given the job of running Rome and its posessions for five years. The titles were renewed for another five years in 38, but the agreement was effectively dead within a year.
The second triumvirate defused the intense rivalry between Antony and Octavian, which was threatening to turn into civil war. This is not to say that it was bloodless. Each member added the names of his enemies to a list of Romans to be proscribed, their wealth confiscated, and their lives forfeit. Marcus Tullius Cicero, long Antony's enemy, lost his life in the subsequent purge.
Although there were three men in the triumvirate, Lepidus never held the power that Antony and Octavian did. By 42, those two had divided control of Rome's colonies and possessions, with Antony in the east and Octavian in the west.
Lepidus, the minor partner in the triumvirate, tried to take over Sicily for himself in 36. Octavian crushed him easily, but let him live. He died peacefully in 13 BC, a total nonentity in Roman politics.
Meanwhile, trouble was also brewing between Antony and Octavian. The triumvirate had been strengthened by the marriage of Antony to Octavian's sister Octavia. In 36, however, Antony abandoned Octavia for Cleopatra, who was trying to regain Egypt's independence. By 32, Octavian had obtained Senatorial consent to dissolve Antony's command in the east, and the second civil war in two generations was underway. At the Battle of Actium, in 31 BC, Antony was deserted by Cleopatra and defeated by Octavian. Both Antony and Cleopatra committed suicide before Octavian could capture them.
Within two years of the defeat of Antony, Octavian was given the title Augustus by the Senate. Under the guise of restoring the Republic, he founded the Empire.