It prevents JSON hijacking, a major JSON security issue that is formally fixed in all major browsers since 2011 with ECMAScript 5.

Contrived example: say Google has a URL like mail.google.com/json?action=inbox which returns the first 50 messages of your inbox in JSON format. Evil websites on other domains can't make AJAX requests to get this data due to the same-origin policy, but they can include the URL via a <script> tag. The URL is visited with your cookies, and by overriding the global array constructor or accessor methods they can have a method called whenever an object (array or hash) attribute is set, allowing them to read the JSON content.

The while(1); or &&&BLAH&&& prevents this: an AJAX request at mail.google.com will have full access to the text content, and can strip it away. But a <script> tag insertion blindly executes the JavaScript without any processing, resulting in either an infinite loop or a syntax error.

This does not address the issue of cross-site request forgery.