What is transmigration of soul?

The process of transmigration is very subtle. The spirit soul is invisible to our material eyes. It is atomic in size. After the destruction of the gross body, which is made up of the senses, blood, bone, fat, and so forth, the subtle body of mind, intelligence, and ego go on working. So at the time of death, this subtle body carries the small spirit soul to another gross body. The process is just like air carrying a fragrance. Nobody can see where this rose fragrance is coming from, but we know that it is being carried by air. You cannot see how, but it is being done. Similarly, the process of transmigration of the soul is very subtle. Living entity takes birth after a gradual process of evolution through 8,400,000 species of life, including 900,000 aquatic species, 2,000,000 non-moving species such as vegetables, 1,100,000 reptile and insect species, 1,000,000 bird species, 3,000,000 beast species, and 400,000 human species.

According to the condition of the mind at the time of death, the minute spirit soul enters into the womb of a particular mother through the semen of a father, and then the soul develops a particular type of body given by the mother. It may be a human being, it may be a cat, a dog, or anything. As explained earlier there are 8,400,000 different forms of life, you can enter any of them, according to your mental condition at death. What we think of at the time of death depends on how we act during our life. As long as we are in material consciousness, our actions are under the control of the material nature, which is being conducted in three modes: goodness, passion, and ignorance. These modes are like the three basic colours – yellow, red, and blue. Just as one can mix red, yellow, and blue to produce millions of colours, the modes of nature are being mixed to produce many varieties of life. To stop the repetition of birth and death in different forms of life, we must transcend the covering of material nature and come to the platform of pure consciousness. But if we do not learn the transcendental science of Krishna consciousness, then at death we must transfer to another body, either better or worse than our present one. If we cultivate the mode of goodness, then we are promoted to the higher planetary system, where there is a better standard of life. If we cultivate the mode of passion, then we will remain at the present stage. But if out of ignorance we commit sinful activities and violate nature’s laws, then we will be degraded to animal or plant life. Then again we must evolve into the human form, a process that may take millions of years. Therefore a human being must be responsible. He must take advantage of the rare opportunity of human life by understanding his relationship with God and acting accordingly. Then he can get out of the cycle of birth and death in different forms of life and go back home, back to Godhead.

Source: A.C. Bhaktivedanta Swami Prabhupada (2012 edition), “Message of Godhead”, Page 32
A.C. Bhaktivedanta Swami Prabhupada (2014 edition), “The Science of Self-Realization”, Page 32 & 183