Melvin Morse is a children's doctor who has sometimes had to rescue children in emergency situations, like drowning. Sometimes these children would be clinically dead for 10 minutes or longer, and when they came back to life, they would tell him about floating above their body and watching the rescue, or meeting family members who had died, or seeing a wonderful light. This is called a "near death experience", sometimes abbreviated as "NDE". If the children were too young to describe their experience in words, Dr. Morse asked them to make a drawing of it.
Dr. Morse, being trained as a physician, knows that modern science wants to explain all NDE's as something electrical or chemical that's still happening in the brain while a person is clinically dead. Science wants to say none of it is real. But after talking with these children, Dr. Morse thinks it's not that simple. He believes the experiences are real, but he also believes there is some part of the brain that specifically has to do with experiencing the after-death, or non-physical, world.
If it is proven that a person's awareness continues after their physical body dies, then it is not too big a step to say that the spiritual part of a person could reincarnate, or come back into a new body. There are many cases where NDE's have been proven to be real. People have temporarily died on the operating table, and when they come back to life, they tell the hospital staff exactly what the rescue looked like--from above! Sometimes they will also say what was happening in nearby hospital rooms, and in one of these cases, the woman, in her regular physical life, was blind, but could see in this way during the NDE.