I see that most of big websites are returning javascript objects instead of pure HTML output, and renders it client side.
What are the advantages of using this approach? (and I think they are when used by Google, FB and others).
I think that one of the advantages is that it doesn’t “freezes” the browser when inserting new html into the page. Freeze problem
Also is it easy to transfer / process it if you have a good javascript API.
Do you know others?

That is the JSON data format, not JavaScript objects (although the syntax is compatible).
JSON is:
The particular example you give has embedded HTML. Presumably the request is for more then a single piece of content to insert into a single part of the page.