What was the significance of nuclear testing in the development of the Internet?

I don't know that it had any. The Internet was originally developed so that the US Department of Defense could communicate better with researchers working on DOD projects. I would assume some of those projects may have involved nuclear testing.

What is the significance of ARPANET in relation to the development of the Internet?

What is the significance of ARPANET in relation to the development of the Internet?

Arpanet was the DOD initiative I referred to. It became the Internet!

You can easily find details by plugging ARPANET into your favorite search engine.