First, watch - description later:
The comet in the video is C/2011 L4, also known as Pan-STARRS after the telescope on Maui that discovered it. Earth, as labeled in the video, is far in the background, so there's not really any interaction despite the apparent shadows that occur when Earth appears to cross the comet's tail - it's simply a matter of Earth being a lot brighter than the diffuse gas and dust released by a comet. Also, the solar release seen in the video probably wasn't in the direction of Earth.
The space probe that captured the video is one of the two NASA STEREO solar observatory probes that orbit the Sun close to and a little bit inward of Earth's solar orbit. They are part of a significant and growing network of probes and Earth-based observatories that coordinate to monitor solar activity for flares and coronal mass ejections (CME's, like the one in the video).
Beneath all logic, all numbers, all monetizable motives and words, there are simply things like this that in themselves fully and sufficiently justify space exploration. Anyone who can watch that and not understand, or dismiss the universe as a series of "pretty pictures," will never get it - never get the reality that these small images we see in front of us on screens are, in fact, unimaginably larger than we are, as real if not more so than we are, and are the context of our existence. In that image of Earth is you - you are in that picture! (Or at least those of us on the side of the planet facing the probe at the time).
6:41 AM PT: As it has been pointed out to me in comments, since the amount of time covered in the video is 5 Earth days, we are in fact all in it.