The Satellaview was an add on for the Super Famicom made by Nintendo themselves. Althought it is commonly believed that the system was made in part by Bandai, and hence the BS naming convention appears, but the system's alternate name the BS-X is apparently relating to "Broadcast Satellite", a Japanese Satellite TV network. I have the none involvement of Bandai on very good authority but feel free to provide evidence to the contrary. The exact date that the system was released is not clear, but most guesses and the sketchy information I have found place it at about a 1991 release date. UPDATE!!! Servo5678 has pointed me to a site which says that the system broadcast from 23rd April 1995 to June 30th 2000. This seems to conflict with other sources I have, but it is from a very reputable Nintendo site, so chances are it is true. The system was only ever released in Japan, which is why you are unlikely to have heard of it.
The add on looked similar to the ill fated 64DD add on developed for the Nintendo 64. It was a large base unit which attached to the bottom of the SNES and connected to the console using a port. The back of the new unit had an AC adaptor and an AV slot. This base unit contained 512k of RAM to supplement that of the SNES. The OS of the BS-X was held in a 1 Megabit ROM chip inside the base unit, and there was also 256k of Flash memory inside, which stored downloaded data in case the user had not bought the additional peripherals that the machine was released alongside.
These additional peripherals were a Game Boy lookalike cartridge which plugged into a BS-X Special Broadcast Cassette, a device which looked exactly like a Super Game Boy. This small cartridge held 1 Megabit of Flash RAM.
The point of the BS-X was to download, store and play data downloaded from the Japanese St-GIGA satellite television system. The data was available to download at certain times only, rather like a pay per view film on Television. As well as normal programmes, the St-GIGA channel featured at certain times game data to download. This data took the form of new levels, characters, moves, demos, etc. You could only download each file at a certain time, for example only during a certain hour, once a week. All downloads were free, but the costs were recuperated by forcing the player to watch adverts while their files were downloading. And there was plenty of time for adverts, as well - apparently sometimes it took as long as 9 minutes to change levels in a game, because of all the new data being downloaded.
The system apparently costed about $150, or about 14 000 yen. The memory cartridge cost another $30, and the Super Game Boy style device cost another $50. As well as all this, it was necessary to have a subscription to St-GIGA, the television channel that all the data was downloaded from. I have no information as to how much this cost, but I am guessing a fair amount.
After paying all that money, you would probably be expecting some games. Nintendo didn't disappoint, but it wasn't all from them - companies like Square and Enix also supplied software. I have read rumours that a multiplayer version of the Dragon Quest series was on the cards, but I have no idea whether it was ever released. How a multiplayer game would be possible on a one way satellite link is unsure, but it may have used the phone line either way.
Thankfully, plenty of games were released for the system. Somehow, a lot of them were dumped by some intrepid emulation fiends. These games can be found floating around the Internet, but they are so obscure that only the biggest ROM sites will carry them. I'm not sure of the exact number of ROMs that the system had, but if you find a ROM with the BS prefix, then it came from the Satellaview. Some games were released both on the BS-X, and then as normal SNES games. Cu-On-Pa is an example of this - rom sites will list both "Cu-On-Pa" and "BS Cu-On-Pa". Some of the best games released on the system were from the Zelda series. See BS Zelda for further details.
Unfortunately, most of the games released on the BS-X are unplayable in their unchanged ROM forms. Luckily for us, a world full of hackers works tirelessly (almost) to provide us with playable versions of the games. BS The Legend of Zelda is one example of this. BS F-Zero 2 is actually playable with no patches, but it is slightly corrupted. Overall, though, remember that in the case of Nintendo games, many of the best ones never made it out of Japan (this, this, and this spring to mind) so many of the games on the BS-X are guaranteed to be pure gaming gold. I'll update as I find some more good ROMs from the system. In the meantime, find and play this.
There are some nice pictures and info at the first website I cite below - good reading if this doesn't enlighten you enough.
This is by no means the only Satellite download video games system ever - the Nintendo 64 linked up to the 64DD could access Randnet, and for Sega consoles there was the Sega Channel.
Thanks to archiewood for some corrections.
Thanks to yerricde for informing me about the Sega Channel.