What is this, and why is it bothering me?

I came into work and found this. I know this is a meme here at this point, but I actually haven't done anything with Chrome in days. It was open and now it's asking for permissions. Will saying yes or no break anything? What is it talking about, even? What does a browser need local network connections?

I came into work and found this. I know this is a meme here at this point, but I actually haven't done anything with Chrome in days. It was open and now it's asking for permissions. Will saying yes or no break anything? What is it talking about, even? What does a browser need local network connections?