How did the location in the mediterranean lead to the development of a Greek empire

There was no Greek empire. The Greek world comprised hundreds of independent city-states, which sometimes came together in temporary leagues.

If you refer to Alexander the Great, the answer is Greece being next door to Asia and in particular next door to the Persian empire. Greek relations with Persia had been tense since the Persians had tried to invade Greece. Persia also held a part of Thrace on the Balkan coast, next door to Greece. Alexander’s policy was war and he defeated this empire. His own empire was basically a taken over Persian empire and extended over that area, apart from an area north of the Caucasus mountain and not extending north of Afghanistan as much.
This empire was so big that it was then divided between the Ptolemaic kingdom (Egypt), the Seleucid empire (the Asian possessions minus the northern coast and the eastern part of Anatolia, that is modern Turkey). the kingdom of Pergamon, the mentioned parts of Anatolia not under the Seleucids and Thrace) and Macedon (Greece minus southern Thrace and Epirus, which remained separate).