The Sega 32X was a console / add on released for the Sega Mega Drive in 1994, and was discontinued in 1995, due to it being a commercial failure.
It had a few games released for it, and it powered up the Mega Drive's power from 16 bit to 32 bit. It played cartridges, and Mega Drive cartridges could be played through the 32X. Owners of the Sega CD/Mega CD could also play Sega Mega CD 32X games, but these were not very common. The 32X took it's own power supply, along with the Mega Drive's power supply. It also required it's own TV lead, with a lead from the Mega Drive into the 32X, and a cable into the TV from the 32X. Without the cable from the Mega Drive into the 32X, the sprite layer is completely invisible. The 32X also required different cables to be used with either the Model 1 or Model 2 Mega Drive.
Games that were released on the 32X included Doom, Virtua Fighter, and many more third party releases, but it didn't see even as many games as the Sega CD/Mega CD.
The reason why the Sega 32X failed was because hype was being generated for Sega's new standalone console, the Sega Saturn. It also retailed for a very high price, and was released late in the Mega Drive's life. Third party support was also low for the 32X, with cartridges being considerably more expensive to make than the new CDs, for the Sega Mega CD and Saturn.
The console sold less than a few million units, and generally sells nowadays for around £/$ 50 on places such as eBay.