Bandha in Hinduism is derived from the Sanskrit root word ‘bandh’ meaning bond, fetter or tie. The meaning of Bandha is bondage and is used to describe the existential state of being who is in the grip of subject-object relation and thereby undergoes the continuous cycle of births and deaths, i.e. samsara.
Bandha in Hindu religion refers to the individual self who always thinks in terms of subject and object, and thereby is subjected to birth and rebirth. It is in this sense that the world bandha is translated as knot, bondage or slavery, etc.
The ultimate aim of the human being, therefore, is to liberate itself from the bandha of duality and realize its inherent unity which is moksha.
In Yoga Darshana of Sage Patanjali, Bandha is the self’s identification with the mental fluctuations caused by avidya (ignorance), asmita (egoism) and abhinivesha (attachment to oneself resulting in clinging to bodily enjoyments and the fear that one might be cut off from all of them by death).
According to Advaita Vedanta, the jiva (individual self) is in bondage because it does not know its true nature. When the veil of ignorance is removed by true knowledge, it is liberated.
Bandha in Jainism
According to Jainism, bondage is due to karma – the activities of the body-mind complex as influenced by passions. The bondage has two stages – bhava bandha and dravya bandha.
Bhava bandha refers to the bondage caused by passion and dravya bandha connotes the entanglement of the being on account of its attachment to matter which is the being takes up in accordance with its karma.
Bandha in Buddhism
Banda is also used to mean dukha (suffering). The theory of pratityasamutpada (dependent origination) of Buddhism explains the causes of suffering and the individual’s chain of bondage to the wheel of birth and death.
One is in the grip of samsara when the mind becomes attached to worldly things such as thoughts, pleasures and pains.
According to Buddhism, one is liberated only when one’s mind is completely detached from objectivity, necessity, invariability and conditionality.
Source - notes taken from Encyclopedia of Hinduism Volume II (IHRF) page 121 - 122