For centuries Greece was occupied by the Ottoman Empire. Piece by piece they liberated themselves in the 19th en 20th century. Their goal was to ‘liberate’ also the areas on mainland Turkey, over where many Greeks lived, and to make Constantinople, present day Istanbul, their capital (instead of Athens). Many Greeks and Armenians lived in Constantinople, in 1900, from the million people living in Constantinople less than 50% was Muslim.
By the treaty of Sevres (1920) large parts of mainland Turkey were indeed assigned to Greece (Troas and Iona). The Greeks started a war to gain even more land, but the Turks, led by Ataturk, counter attacked and the Greeks lost all the land the had gained before. The red dotted line show roughly the advance of the Greek troops c.q. the proposed great Greece ('megali Hellas').