The Tet Offensive was considered to be a psychological victory for the Viet Cong and for North Vietnam even though it was a military defeat for them. The reason for this was that it demoralized the Americans and led them to lose faith in their leaders and in the war. It was soon after this that President Johnson decided not to run again for the presidency.
In the time before the Tet Offensive, the American political leaders had constantly been reassuring the country that the war was going well. They had been putting forth a narrative about how the war was just about won and about how the enemy was running out of the ability to mount any serious resistance. When the Tet Offensive opened up, it became clear that the US leaders had been wrong. The communists did not win the Tet Offensive militarily. However, they did prove conclusively that they were not finished as a force. Because they were able to prove this, they demoralized the Americans and helped turn American public opinion against the war. In this way, the offensive was an important psychological victory.