What part of a person goes on into eternity when they die?
The part of a person that goes on into eternity is the immaterial, invisible self: the mind, the will, the emotions, and the personality. The body is only a temporary earthly tabernacle or tent that dissolves and returns to the earth, while the real person continues eternally.
Les explains from 2 Corinthians 5 that the earthly house is the body, described in the Greek more like a tent—a temporary dwelling place. The body is just a dwelling place for the real you and me. The real us, the part that goes on into eternity, is the invisible mind, will, emotions, and personality. When this earthly tabernacle dissolves and goes back into the earth from which it came, that does not stop us because we are eternal. Instead, we have a building of God, a house not made with hands, eternal in the heavens.
For we know that if our earthly house of this tabernacle were dissolved, we have a building of God, an house not made with hands, eternal in the heavens.