What are nested quotes? Let me illustrate.

Previously, when quoting someone in a conversation who quoted someone else, your response would only only include the quote of the person who you're directly responding to and the previous quote would be lost, thus interrupting the conversation.

When I respond to Bogon by quoting his comment:
Snap28.jpg

the comment he quoted would be lost:
Snap29.jpg

With nested quotes now available, the first quote that Bogon responded to is included in my quoted reply:
Snap30.jpg

The best part about this is that nothing different is required on your part. You still just hit the "Reply With Quote" button.