When this resident of the body, the embodied one, detaches from the body, when he is liberated from the body, what remains here? This is in truth That.

This verse describes death and liberation from the body.

Asya visraṃsamānasya — when this one detaches. Letting fall, releasing.

Śarīrasthasya dehinaḥ — of the resident of the body, the embodied. Dehin = the one who has a body.

Dehād vimucyamānasya — when liberated from the body.

Kim atra pariśiṣyate — what remains here? If the Ātman is liberated from the body, what remains?

Etad vai tat — this is in truth That.

The verse indicates that at death, the Ātman is not destroyed; it remains as Brahman. This is the teaching of immortality.