Question

what is the chemical nature of distilled water

Answer 1

H2O will be the chemical formoula

Answer 2

Neutral I am a little uncertain as to what this question is about. Water (pure) is water, distilled or other wise.

You can purify water by lots of different means - simple distillation up to nanopure systems that run it through reverse osmosis, ion exchange, activated charcoal, etc. These efforts all attempt to render water free of contaminants. None of them render water pure though they come very close.

The chemical nature of water, pure or impure, is not really affected.