The Second Triumvirate coalesced and then broke down because of political ambition.
The triumvirate formed after the assassination of Julius Caesar. It formed because Octavian and the others wanted to keep power in their own hands and out of the hands of those who had conspired to kill Caesar. Once they won that battle, however, they were too ambitious to continue to share power with one another. Instead, Octavian and Antony pushed Lepidus out and divided the empire between them. When that wasn't enough they fought one another, with Octavian eventually winning and becoming Augustus, the first emperor of Rome.
Most of this is dramatized in Shakespeare's Antony and Cleopatra. According to Shakespeare, the rift between Octavian and Antony was caused by Antony's obsession with Cleopatra.