What is mDNSResponder - and why is it running on my Mac?

mDNSresponder is a process required for discovering Macs used for Back to My Mac as well as related Bonjour device discovery features. It was briefly superseded by the ill-fated discoveryD which never worked right.

Like many other macOS components it’s required for proper operation, so make no attempt to delete it or prevent it from working.

It is an essential piece of system software. There is nothing wrong. If you start looking for things you are going to find a lot that you don’t know, and don’t need to know. Just enjoy your mac. Or if you are having a problem describe it clearly so you can get adequate help.