1 It's a quote from Aliens.  It's also an once-popular internet meme, particularly on Fark.

2

An example of it's use would be something like:

Person A: "I've got a case of uveitis in my eye."

Person B: "We'll have to nuke it from orbit, it's the only way to be sure."

3

The "Game Over, Game Over" alt text is from this scene.

And like Duck said, anything that's troublesome or just outright disgusting needs to be nuked from orbit to be sure.

4 I'm familiar with the term; but I first ran into it in something a guy from Microsoft said about infected computers. The term "nuke it from orbit" in computers means to completely wipe the HD and reinstall the OS from scratch.

5 I wonder where they got the picture from. It's gorgeous.

6 Which makes sense; computer techs are among the most likely to pick up such a meme.  It's popular enough, though, that I've never confused any non-tech people by using it.

I would highly recommend the movie; it's one of Cameron's best.

7 Look at the source with ^U, it gives the origin for the picture, and also shows the Google Analytics code.

8

The flickr accoutn linked at the bottom of the page says it's from a French nuclear test called Licorne. Googles the only resources in this case, because Wikipedia just forwards to the unicorn entry.