Our Gemara on Amud Aleph quotes one of the key verses in regard to sexual prohibitions:

ויקרא י״ח : כט

כִּ֚י כׇּל־אֲשֶׁ֣ר יַעֲשֶׂ֔ה מִכֹּ֥ל הַתּוֹעֵבֹ֖ת הָאֵ֑לֶּה וְנִכְרְת֛וּ הַנְּפָשׁ֥וֹת הָעֹשֹׂ֖ת מִקֶּ֥רֶב עַמָּֽם׃

⁦All who do any of those abhorrent things—such persons shall be cut off from their people.

The verse describes the consequence of kares, being “cut off from the people”. What does this really mean? Fortunately we have a sage of the stature of the Ramban (Op. Cit.) who explains what kares is in great detail.  In fact, it actually is three different consequences, depending on the severity of the sin.

Based on the language of the verse, kares can either mean early death before age 60, or losing out on the afterlife, or both. 

The texts that state “that person shall be cut off” (Vayikra 17:4 and 9) is referring to his lifespan, not his soul. This is the mildest form of punishment, as only his life in this world is affected.

The texts that state that “His soul shall be cut off” (Vayikra 18:29 and 22:3) are referring to loss of life in the afterlife. In fact, Ramban says he may live to a long and healthy old age in this world and be unaware of the doom that awaits him.

Then there are texts that use a double language, הכרת תכרת “He shall be cut off, and cut off” (Numbers 15:31). The double cut off implies a shortened life time in this world, and loss of the world to come.

The Ramban adds that though the Torah does not mention the afterlife explicitly, the verses about kares are strong indicators that there is a realm of existence that is beyond the physical world. He reasons, it is a given that the soul is eternal and exists beyond the physical realm. The Torah goes out of its way to point out that certain sinners, as a punishment, will lose their soul’s existence. However, the default then is the eternality of the soul.

One more idea about the soul and punishment that is powerful comes from Rav Chaim Volozhin (Nefesh HaChayyim 1:6). When a person performs a Mitzvah, or sadly, commits a sin, it is immediately felt in his soul. Because the person is distracted and occupied in earthly matters he doesn’t notice the pain and suffering or bliss his soul experiences on an ongoing basis. In other words, Heaven and Hell are not for the afterlife but rather, it is going on right now.