BG Chap 15 - The jīva is eternally an aṁśa of the Lord - II
The fragmental portion of the Supreme Lord is not like some material broken part. We have already understood in the Second Chapter that the spirit cannot be cut into pieces. This fragment is not materially conceived. It is not like matter, which can be cut into pieces and joined together again. That conception is not applicable here, because the Sanskrit word sanātana ("eternal") is used. The fragmental portion is eternal.
Through the similarity of its reflected image, one can understand the real nature of an object, by carefully discerning the substratum of the reflection— as in the case of understanding about an object by seeing its reflection in water. Therefore, the jīva can be said to be a secondary form of Brahman and is thus called a part or aṁśa of the Brahman. It is similar to saying that one hundredth aṁśa of the moon planet is the planet of Venus (since it has a hundredth of the brilliance, but is not an actual portion of the moon). Being a part means that a real object exists in a particular, limited place. Brahman is the possessor of śakti, and another real entity is the śakti of Brahman. The śakti of Brahman is the jīva. Kṛṣṇa had already explained that His superior energy is the jīva (7.5). Therefore because the jīva exists in a particular, limited place (separate from the Lord but similar to some degree), the jīva is called a part of the Lord.