Error in launching Chrome Extension for a specific page

You are adding a browser action popup, which adds a button to the top-right of your browser. (It’s probably invisible because you haven’t specified an image for it. There should be some empty space to the right of your address bar; try clicking it to see your Hello.html in a popup.)

What you want is a content script. Content scripts can get injected into every page that Chrome loads. You can use the matches and exclude_matches sub-items in your manifest file to specify which pages get your injected script.

{
  "name": "Hello",
  "version": "1.0",
  "description": "Says hello to Google",
  "permissions": ["tabs", "*://*.google.com/*"],
  "content_scripts": [
    {
      "matches": ["*://*.google.com/*"],
      "js": ["hello.js"]
    }
  ]
}

Make sure you rename Hello.html to hello.js (and get rid of the <script> tags).

Note also that I changed your http://*.google.com/ to *://*.google.com/* so that it will apply to Google over HTTP and HTTPS (and the trailing * ensures that it will apply to all pages on google.com, not just the main page).