Firebase CLI: "Configure as a single-page app (rewrite all urls to /index.html)"

That option simply sets a flag in the firebase.json file to redirect all URLs to /index.html.

"rewrites": [ {
  "source": "**",
  "destination": "/index.html"
} ]

See the documentation of Firebase Hosting for more information, which also contains this fuller example:

"hosting": {
  // ...

 // Add the "rewrites" attribute within "hosting"
  "rewrites": [ {
    // Serves index.html for requests to files or directories that do not exist
    "source": "**",
    "destination": "/index.html"
  }, {
    // Serves index.html for requests to both "/foo" and "/foo/**"
    // Using "/foo/**" only matches paths like "/foo/xyz", but not "/foo"
    "source": "/foo{,/**}",
    "destination": "/index.html"
  }, {
    // Excludes specified pathways from rewrites
    "source": "!/@(js|css)/**",
    "destination": "/index.html"
  } ]
}

Full example:

{
  "hosting": {
    "public": ".",
    "rewrites": [
      {
        "source": "**",
        "destination": "/index.html"
      }
    ]
  }
}

If you set it to yes, then all invalid URLs like www.example.com/some-invalid-url will be redirected to index.html of your site which is a good thing. You can also set it to your custom 404.html.

firebase.json

{

  "hosting": {
    "public": "pubic",
    "ignore": ["firebase.json", "**/.*", "**/node_modules/**"],
    "rewrites": [
      {
        "source": "**",
        "destination": "/index.html"
      }
    ],
    "cleanUrls": true
  }
}

Bonus: set the cleanUrls to true to remove .html extensions from your deployed website urls else all urls without .html will redirect to index.html.