Acharya Prashant uses the metaphor of a monkey chained since birth to explain the nature of human bondage and identity. The monkey has become so accustomed to its chain that it considers the chain to be its third hand, a part of its own body. When the monkey desires freedom, it mistakenly tries to achieve it while retaining the chain, not realizing that the chain itself is the very thing preventing its liberation. The speaker emphasizes that the monkey's definition of 'I' includes the bondage, making true freedom impossible as long as that identity is maintained.