Back in the early days of the IBM PC, the main bus (8 bits wide) was extended out to a number of slots, into which expansion cards could be added. This was called the ISA bus (Industry Standard Architecture).
When the PC-AT came out, there were two issues. Firstly, the processor was now a true 16 bit processor, and secondly, the main bus was running too fast to be synchronised to external cards. So the bus was extended to 16 bits by adding a small extra slot onto the end of the 8 bit slot, and it was also decoupled from the main processor bus to avoid the synchronisation issues. The new slots could take both 8 bit and 16 bit cards quite happily.
Then, in the late 1980's, the IBM PS/2 came on the scene. IBM wanted to provide something more powerful than ISA, and they came up with MCA. This was a 32 bit bus, which also featured bus mastering. This basically allows one card to take control of the bus and talk directly with other cards or memory, saving processor time. Unfortunately, IBM made two mistakes. Firstly, this was totally incompatible with ISA, so everybody would have to buy new (and much more expensive) MCA cards for their machines. Secondly, they charged a fortune for licensing the slots, so very few companies made MCA machines.
However, some companies (most notably Compaq) realised there was a need for a more powerful bus, and they came up with EISA - Enhanced Industry Standard Architecture. An EISA slot, at first sight, looked exactly the same as a 16 bit ISA slot, and indeed, it was fully backwards compatible and could take 16 bit and 8 bit ISA cards.
What you didn't see, though, was a second set of contacts underneath the first set. A row of lugs stopped 16 bit cards going deep enough into the slot to touch these, but 32 bit EISA cards had notches which allowed them to go the whole way down.
EISA had the high power and bus mastering capabilities of MCA, but without the compatibility issues. Additionally, it was less expensive to license (although still not cheap). It was a common sight in servers, being used for high end (for the time) SCSI and network adapters.
However, most people simply didn't need that sort of power in general desktops, so EISA never really took off. Of course, cut to a few years later, and VLB and PCI came around, which are now ubiquitous.
That said, you could until quite recently still find EISA slots in high end Compaq servers, alongside the PCI slots.