Incarnation means physical life, which occurs when a soul anchors itself in a physical body for a lifetime.
Reincarnation means returning to physical life in a new body after completing one or more previous lifetimes. Apparently, we each live many lifetimes.
Life can be understood as a continuous stream which changes form, but not its essence, through transitions such as birth and death. The soul exists prior to any incarnation, and does not die when the body ceases to function.
“Soul” has many definitions. I use this term to refer to the subtle and complex, multidimensional energy structure which contains our eternal spiritual essence.
Powerful evidence does exist. For example, Dr. Ian Stevenson has investigated and thoroughly documented hundreds of cases of young children, each of whom spontaneously recalled a very recent previous life. In each of these cases, the child’s memories were so precise and detailed that it was possible to verify that the previous personality (the person the child said she or he had been before) actually existed.
Additional evidence linking the children to their past-life personalities was substantial. For example, when brought to the past-life villages, many of these children unerringly found their way to their former homes in territories where they had never been before (in the current lifetime). They recognized and correctly identified surviving people whom they had known in the previous life, and even revealed family secrets.
For more information about Ian Stevenson’s work and other evidence for reincarnation, you could start with Stevenson’s “Twenty Cases Suggestive of Reincarnation”; Joe Fisher’s “The Case for Reincarnation”; Dr. Helen Wambach’s “Reliving Past Lives: The Evidence Under Hypnosis”; or Carol Bowman’s “Children’s Past Lives” (an outstanding book which summarizes previous research, and much more).
For an in-depth examination of the nature of reincarnation (including evidence, historical and cross-cultural views, and implications), I recommend Hans Ten Dam’s “Exploring Reincarnation.” Dr. Brian Weiss gives a profound, spiritually-oriented and practical introduction to the topics of reincarnation and past-life therapy in his first two books: “Many Lives, Many Masters” and “Through Time Into Healing.” Weaving together multicultural esoteric teachings with knowledge and experience in psychotherapy and bodywork, Jungian analyst Dr. Roger Woolger gives a harrowing yet brilliant account of extreme karmic patterns in reincarnation and their resolution through past-life therapy in “Other Lives, Other Selves.” Edgar Cayce’s unique perspective is revealed in Noel Langley’s “Edgar Cayce on Reincarnation” and Lynn Sparrow’s “Reincarnation: Claiming Your Past, Creating Your Future.”