Answer
The gross body (sthula sharira) is that body in which the hands, feet, heart, lungs, brain, and other organs exist in their gross, physical form. In ordinary language, this is simply called 'the body.' It can be seen and touched, and it is this body that undergoes death.
The subtle body (sukshma sharira) is situated within this gross body. After the death of the gross body, it continues to exist for a period without any gross body. The subtle body does not undergo 'death' in the ordinary sense. When the subtle body is ultimately destroyed, the Atman attains moksha (liberation).
The ultimate fruit of all spiritual practice is the destruction of the subtle body, so that the Atman may attain moksha. In Vedanta, this is called the sukshma sharira (subtle body), while in Sankhya Darshana, the same is called the linga sharira.
The causal body (karana sharira) is not mentioned in Sankhya Darshana, but it is described in Vedanta Darshana. Nevertheless, the general view is that calling it a 'body' is not quite appropriate. It is usually referred to as ajnana (ignorance) or avidya (nescience). In simple terms, it is the 'glue' that keeps the Atman bound to the subtle body, and through the subtle body, to the gross body. In other words, the cause of the Atman's bondage to the world is this very ignorance or avidya.
The day this glue is destroyed, the Atman's connection with the subtle body (and the gross body) is severed. Then the Atman, having attained moksha, reaches the supreme destination, becomes forever free from the world, escapes the cycle of rebirth, and attains nirvana.
The subtle body or linga sharira is said to be composed of 17, and sometimes 18, tattvas (principles). These include manas (mind), buddhi (intellect), and ahankara (ego); the five jnanendriyas (organs of knowledge) and the five karmendriyas (organs of action) in their subtle forms; and the five tanmatras (subtle elements).
The Five Tanmatras: The five tanmatras, in Indian philosophy — especially Sankhya and Yoga — refer to those subtle principles from which the gross material world is subsequently formed. In brief, the tanmatras are the subtle seeds of the qualities experienced through the senses.
1. Shabda Tanmatra (Sound) — the subtle cause of sound — related to the ear (hearing) — from this, the element of Akasha (space/ether) arises. 2. Sparsha Tanmatra (Touch) — the subtle cause of touch — related to the skin — from this, the element of Vayu (air) arises. 3. Rupa Tanmatra (Form) — the subtle cause of visual form — related to the eyes — from this, the element of Agni (fire/light) arises. 4. Rasa Tanmatra (Taste) — the subtle cause of taste — related to the tongue — from this, the element of Jala (water) arises. 5. Gandha Tanmatra (Smell) — the subtle cause of smell — related to the nose — from this, the element of Prithvi (earth) arises.
This sequence can be understood as follows: Prakriti -> Tanmatras -> Pancha Mahabhutas (five great elements) -> the gross world.
That is, everything we experience through the senses has, at its root, first the tanmatras, then the pancha mahabhutas, and finally this visible world.
Exploring a little further: the subtle body stores all the samskaras (impressions), memories, and sentiments from previous births. This subtle body is our true worldly identity. After the death of the gross body, it is this subtle body that enters a new gross body, and in this way, the journey continues from birth to birth.
When tattva-jnana (knowledge of the ultimate reality), atma-sakshatkara (Self-realization), or atma-prapti (attainment of the Self) occurs, avidya is destroyed. The glue that had kept the Atman attached to the subtle body is dissolved. Consequently, the Atman becomes free from the cycle of birth and death and attains moksha.
Thus, among the various layers or coverings of the Atman that are discussed, we have understood the gross body and the subtle body, while the causal body is best understood not as a 'body' but as ignorance or avidya.
However, in the Agama scriptures, another type of body — the bhuvanaja sharira — is also mentioned. When the subtle body leaves the gross body and travels to svarga (heaven), naraka (hell), Shivaloka, Vaikuntha Loka, and so on, it receives a special bhuvanaja body in each bhuvana (realm).
Mahopaadhyaya Pandit Gopinath Kaviraj — a great scholar of Agama literature — writes that the bhuvanaja body obtained in each realm differs according to the nature of that realm. Elaboration of this subject is not necessary here. The bhuvanaja body obtained in naraka (hell) is called the yatana sharira (body of torment). This is a body that can be repeatedly damaged and reconstituted so that the soul may experience torment again and again. For example, if in a particular punishment the body is burned, the same body is reconstituted for the next punishment. The Ramcharitmanas also mentions this yatana sharira.
In some scriptures, the size of the subtle body is also described. According to one description, if the tip of a hair is divided into one thousand parts, and then one of those parts is divided into a hundred parts further, the size of the subtle body is said to be equal to that one-hundredth part.
In the Gita, the gross and subtle bodies, and the Atman's continued attachment to them due to ignorance, are mentioned either directly or by implication, and the principle of attaining moksha by becoming free from both these bodies through the destruction of ignorance is fully supported.