Saṃsāra is not a location or a punishment. It is a condition: the condition of identifying the self with the body-mind, generating karma from that identification, and thereby perpetuating the cycle of experience. Advaita does not escape saṃsāra — it sees through the identification that constitutes it.
The word saṃsāra means "wandering through" — from sam (completely) + sṛ (to flow, to wander). Not a place you are sent to. A flow you are caught in — moving from experience to experience, life to life, driven by the momentum of desire and action.
The mechanism is simple. The self is misidentified with the body-mind (adhyāsa). From that misidentification, desires arise — because the apparently limited self feels incomplete and reaches for what might complete it. From desires, actions arise — karma. From karma, experiences arise — pleasant, unpleasant, mixed. From experiences, new desires arise. The wheel turns.
Saṃsāra is not foreign to you. It is the structure of ordinary experience: waking up wanting something, pursuing it, getting it or not, adjusting the desire, pursuing again. The pleasure fades. The pain passes. Something new is wanted. This is the wheel — not as dramatic cosmological mythology but as the moment-to-moment structure of a life driven by the belief that the self is limited and that something outside it will complete it.
Advaita's diagnosis: the belief in incompleteness is the error. The self is not limited. It is Brahman — unlimited, complete, without lack. What is identified as the self (the body-mind) is limited and does not deliver completeness. But the awareness within which that body-mind appears — that is already complete. The recognition of this is mokṣa: the dissolving of the sense of lack that drove the wheel.
The Bṛhadāraṇyaka 4.4.3–6 contains the Upanishadic account of the mechanism of saṃsāra. It describes the departure of the self at death, its journey through various realms, and its return to a new birth determined by the karma carried. Verse 4.4.5 is precise: sa vai puruṣo kāmamaya — "this person is made of desire." As one desires, so one becomes; as one acts, so one attains. The continuity of saṃsāra is not metaphysical but psychological: the desires and identifications that constitute a personality survive bodily death (as sūkṣmaśarīra, the subtle body) and generate the next birth.
Śaṅkara's commentary on this passage establishes the Advaita framework: saṃsāra is sustained by avidyā (ignorance of Brahman-Ātman identity) operating through kāma (desire). Karma is the mechanism; avidyā is the root. Eliminating karma alone — through perfect renunciation — does not address the root. The root is the misidentification of the self with the body-mind, from which desire naturally arises. The liberating knowledge that removes avidyā removes the root from which desire grows, and thereby ends the generation of new karma. Saṃsāra does not end through exhaustion (karma being cancelled by opposite karma) but through dissolution (the root of karma-generation being seen through).
The Advaita account of saṃsāra has a specific relationship to the Sāṃkhya-Yoga account that is worth examining. In Sāṃkhya, saṃsāra is produced by the confusion of Puruṣa (pure consciousness) with Prakṛti (the material principle including mind and senses). Liberation is the recognition of their eternal separateness. In Advaita, saṃsāra is produced by the confusion of Ātman/Brahman with the upādhis (limiting adjuncts) of the body-mind. Liberation is the recognition of identity — not separation. The diagnostic is structurally similar (confusion between consciousness and its instruments); the remedy is opposite (separation in Sāṃkhya, identity in Advaita). Śaṅkara spends considerable space in the Brahmasūtra Bhāṣya (Chapter 2) arguing against the Sāṃkhya account precisely at this point: if Puruṣa and Prakṛti are eternally separate, the confusion between them is inexplicable. If they are ontologically one (Brahman appearing through māyā), the appearance of confusion — and its dissolution — is structurally coherent.