Truman's claim outlines his belief in idea of the domino theory. The domino theory revolved around the idea that if one country fell to communism, nearby countries would fall as well. Considering that Greece and Turkey were close to the Soviet Union, Truman is worried that these two countries will fall to communism. If Turkey and Greece fall to communism, then other nations near these two countries would fall as well. This is why the president creates the Truman Doctrine, as this law will give $400 million in economic aid to Greece and Turkey.
(credit to Kalahira on here, saw her answer for this question and thought id share it!)