This is the blue shell item available in Mario Kart 64 (and possibly earlier versions; I have not played these).
It is a particularly useful weapon, in that (provided it is not fired off the edge of the track or straight into a wall), will chase around the track after the player coming first. Any other players who happen to get in its way will also be knocked arse-over-teakettle. This makes it nifty for catching up to the race leaders after a few mistakes have left you back at 7th or 8th.
I've noticed that there is almost no chance of picking up this item from the random crystals when you are the player in first position, and only a slight chance if you're elsewhere in the top 4 (in Grand Prix mode). I'm not sure if this is deliberate or just strange chance. There are, however, crystals in some of the levels that will always give out a blue shell, regardless of the position of the player. Most notably, the one atop the large rock, accessible by taking the large jump in the beach level.
When fired, it initially shoots off in whatever direction you're currently facing, so be careful not to waste the shell by slamming it straight into a wall or off into space. After a few seconds, it will work out where the track lies, and dash off down it after the race leader. It generally follows the middle of the track, although will swing out (and sometimes dramatically so) around corners.
As it travels, it makes its distinctive sound. When you hear this sound, it's a good idea to move towards the inside of the track so that it zips past safely.
It is suggested in the Mario Kart bugs node that the blue shell of death cannot be defended against; however this is not so. There are three items that will protect the race leader from a blue shell attack:
Being affected by a Star (invincibility) at the time the shell hits will have the same effect as it does with any normal shell; that is the shell will "die" and you can continue as normal.
Using the Ghost item when the shell is near to hitting you (ie, when it's close enough to hear it) will cause the shell to stop tracking you. It will just zip past, going through you with no effect if you happen to be in its way, and will continue circling the track (I suspect it attacks the 1st position player next time it comes around, but haven't verified this).
The other way to throw off a blue shell attack is to have a blue shell yourself. If you hold a blue shell behind you, it will have the same effect as holding any other shell behind you, except that it will defend against other blue shells as well. If you find yourself in first place and are lucky enough to score a blue shell, keep it with you. If someone else attacks with one, hold it out behind you, and try not to let the attacking shell hit you side-on.