Flesh and blood body
The phrase flesh and blood body appears often, and it simply serves to emphasize the material, actually-existing nature of the bodies that we ultimately are.
While a soul is immaterial -- whether you believe the soul dies with the body, or goes off into some after-life, or enters another body into a re-birth, etc., doesn't change that it's immaterial in nature -- the body is material, made of this earth, its constituent parts and atoms returning to the earth after death.
In a PCE you experience yourself as this very flesh and blood body. You see that this actual body being conscious is what you actually are -- not the soul that you felt yourself to be before. Needless to say this can come as quite a shock and causes many a person to run for the hills.