During the Cold War, there were two sides. One side was the side of the United States. The other side was aligned with the Soviet Union and was generally communist.
The non-aligned movement consisted of a number of countries that did not want to have to take sides. They did not want to align themselves with either the Soviet Union or the United States. The major countries that were involved in this movement were India and Egypt. Another major country in the movement was Yugoslavia. The movement was formally started at a summit in 1961, but it had been developing since the mid-1950s.
Non-aligned in context of the cold war refers to the countries that maintained neutrality bot of the the two rival groups involved in the cold war. A group of such nations formed started what they called non-aligned movement.
This group of non-aligned nations, who were all from developing countries, met to form policies for dealing with the major industrial nations. The Non-Aligned Movement originated with a conference held in Bandung, Indonesia in 1955. This conference was attended by 29 Asian and African nations, with the aim of avoiding aligning themselves with either of the two superpowers involved in the Cold War - the United States or the Soviet Union. By the time 1995, when the 11th summit of the movement was held in Cartagena, Colombia, the Non-Aligned Movement membership had grown to 113 countries, mainly African, Asian, and South American.