Vibhūti Pāda · Sutra 38
बन्धकारणशैथिल्यात्प्रचारसंवेदनाच्च चित्तस्य परशरीरावेशः
bandha-kāraṇa-śaithilyāt pracāra-saṃvedanāc ca cittasya para-śarīra-āveśaḥ
By loosening the causes of bondage and knowing the channels of the mind, entry into another body arises.
Bandha is bondage. Kāraṇa is cause. Śaithilya is loosening. Pracāra is movement, channel. Saṃvedana is knowledge. Paraśarīra is another body. Āveśa is entry.
The yogī can transfer their consciousness to another body. This requires two things: loosening what binds the mind to the present body, and knowing the channels through which the mind can travel.
The causes of bondage are the kleśas and karmas that maintain identification with the current body.
The channels are the subtle routes through which consciousness can move: the nāḍīs, space, karmic connections.
This siddhi allows temporarily inhabiting other bodies, experiencing other perspectives, or even permanently transferring at death.
The tantric texts elaborate specific techniques. Some masters supposedly used this power to continue their mission in new bodies.
It is one of the most extraordinary siddhis and also one of the most dangerous if abused.