Harry Truman was deeply involved in the Cold War and had a great impact on that conflict because he was the President of the United States during the earliest years of the Cold War.
Harry Truman was President of the United States from 1945 (when President Franklin D. Roosevelt died) until 1953. It was during this time that the Cold War began. Truman was involved because he was the leader of the United States, which was the leading country on the democratic/capitalist side of the Cold War.
Truman had many impacts on the Cold War. In a sense, you can say that he caused (along with Josef Stalin) the Cold War to begin. If Truman had not been strong in his opposition to the spread of communism, the Cold War might not have started. If, for example, Truman had not issued his Truman Doctrine, which said that the US would help support any countries that were in danger of being taken over by communist forces, the Cold War might not have begun.
Thus, Harry Truman was a very important figure in the Cold War. He was President of the United States when the conflict began and the conflict might not have begun had it not been for Truman.