Why was the conflict between the Soviet Union and the United States described as a cold war?

The conflict between the USSR and the United States was called the "Cold War" because neither side ever directly engaged the other in a military battle. Both the USSR and United States engaged in proxy wars, such as Vietnam and Korea, in which each side backed or directly fought for governments that the other side opposed, with financial and military assistance.

Remember that the Cold War was a struggle between ideologies, in which each side aimed to bring as many other countries under its sphere of influence. The goal for the United States was not necessarily to gain territory, but rather to halt the spread of Communism and to support any and all governments that resisted it and/or aligned themselves with American interests. This strategy, first articulated under The Truman Doctrine, named for President Truman, came to be known as Containment.

The goal for both sides was generally to avoid a direct, "hot war," if possible, because both sides had vast arsenals of nuclear weapons, and each country came to understand that a nuclear war would likely wipe out human civilization. This theory became known as Mutually Assured Destruction. So while the threat of a third world war and a resulting nuclear holocaust hovered over the almost fifty year conflict, both countries went out of their way to avoid that scenario.