Yagnavalkya said: 'Vayu (air) is that thread, O Gautama. By air, as by a thread, O Gautama, this world and the other world, and all creatures are strung together. Therefore, O Gautama, people say of a dead person that his limbs have become unstrung; for by air, as by a thread, O Gautama, they were strung together.' The other said: 'So it is, O Yagnavalkya. Tell now (who is) the puller within.'

In plain words: Yagnavalkya says the thread is air, or the life-breath, which holds this world, the next world and all creatures together. That is why people say a dead person's limbs have come undone. Uddalaka agrees and asks him to explain the inner ruler next.