The numbers track the order that the cells were executed in. So, strictly speaking, you need the numbers to be able to reproduce the output of the notebook's au

The numbers track the order that the cells were executed in. So, strictly speaking, you need the numbers to be able to reproduce the output of the notebook's author. However, I think it's bad practice and pretty uncommon to publish a notebook where you need to execute the cells out of order. So most of the time the numbers aren't useful.