There were three main reasons that the US needed, in President Truman's mind, to intervene in Greece.
First, Greece was very poor. Truman said they didn't even have enough money for bare necessities because of the ravages of the war. Second, they were in the middle of a civil war with a communist insurgency. Third, no one else could help them since the British, who had been helping them before the war, were broke from the war as well.
For these three reasons, Truman believed that US help was necessary. If the US did not help, Greece would fall to the communists. This was the beginning of the Truman Doctrine in which Truman said that
it must be the policy of the United States to support free peoples who are resisting attempted subjugation by armed minorities or by outside pressures.