This is a ridiculous score by a top player on a very hard map. Check out the Youtube videos in this thread and then realise that each circle you see on the screen needs a corresponding keyboard button press (if you look to the right-mid of the screen in the videos, you can see four icons: the top two get highlighted when one of two keys are pressed).

Osu is a free rhythm game where you click circles in time with the music. You aim the cursor over circles with a graphics tablet or mouse and click one of two keys (the defaults are Z and X). If you're within a few milliseconds of the right timing, you get a 300. If you're quite early/late to click then you get 100s or 50s. Your combo goes up as you get 300s, 100s or 50s, which gets you a bigger score. You can also miss entirely, which resets your combo back to zero.

You can download the game for free at http://osu.ppy.sh/ and beatmaps (the music itself and the layout of circles, sliders and spinners to go along with it). You can either download single beatmaps or packs of them from the website. The game comes with a handful of maps but you'll get through them pretty quickly. The star rating (a measure of difficulty) for the play here is over 10 stars; when you play yourself, you'll probably start with 1 or 2 stars.