Tripoli is in the news, but that's not what I'm writing about. Tri-poli is obviously of Greek (also Latin) origin - Tri meaning three and Poli being city. So the name of the city of Tripoli means "three cities".
It gets it's name from the province it is in, Tripolitania, formerly the Roman Province of Tripolitania. The three cities were founded as Phoenician colonies and were named Oea (on the site of modern Tripoli), Sabratha and Leptis Magna. They fell under the sway of Greek Cyrenaica, then later Carthage (another Phoenician colony) and were seized by Rome during the Third (and final) Punic War. At some point this area was split off from the Roman province of Africa, and named after the three cities that were it's main feature. The name stuck, and the city was renamed after the district.