I've done a fair pinch of research on the Macintosh ones, and it is hard to find definitive answers on these usually 10-20 year old products. However the Apple II ones are far better documented, oddly enough being usually 20-30 years old.

Here is my findings:

It is either a PC Transporter:

The PC Transporter card made it possible to run IBM-PC programs on an Apple II Plus or IIe, and, like the software-based emulator programs of today, it widened the available program choices for the Apple II user. It literally created another hardware-based computer within the Apple II, and with the right software (to let this simulated IBM PC know how to use Apple peripherals such as the Disk II drive, paddles, etc.) it would run many programs just as well as on a real IBM PC. (Photo credit: unknown) -http://apple2history.org/museum/peripheralcards_nonapple/'>http://apple2history.org/museum/peripheralcards_nonapple/

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PC Transporter lets an Apple II run MS-DOS programs three times faster than an IBM PC/XT with an Intel 8088-compatible NEC V20. Running in the IBM mode, PC Transporter provides up to 640K of user RAM and 128K of system RAM. Up to 768K of extra RAM is available for Apple programs. It also accepts an optional 8087-2 Math co-processor chip and a lot of other AE accessories. Compatible with II+, IIe, and IIgs. -http://ae.applearchives.com/all_apple_iis/pc_transporter/

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Links:

http://apple2history.org/museum/peripheralcards_nonapple/

http://ae.applearchives.com/all_apple_iis/pc_transporter/

http://a2central.com/1665/pc-transporter-installation-video-now-on-youtube/ (They have an install video)

http://en.wikipedia.org/wiki/Applied_Engineering (Manufacturer, and also maker of other awesome Apple II stuff)

or

A Z-80 SoftCard:

Microsoft's first hardware product was the Softcard, a Z80 coprocessor card that allowed the CP/M operating system to be run on an Apple II. CP/M (which stands for Control Program/Microprocessors, Control Program/Monitor or Control Program for Microcomputers, depending on who you ask) was a popular OS for Intel 8080/Zilog Z80 based systems, and ran on many early microcomputers. It was written in the late 1970's by Gary Kildall, founder of Digital Research, Inc. -http://www.apple2info.net/hardware/softcard/softcard.htm

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The Softcard did not have any memory on it, and instead used the memory installed in the Apple II. It was compatible with most of the standard Apple II expansion cards, such as 80-column video cards, printer cards, serial cards, but they had to be installed in certain slots. Generally, if the Apple II configuration worked with Apple Pascal, it would work with CP/M. -http://www.apple2info.net/hardware/softcard/softcard.htm

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Links:

http://apple2history.org/museum/peripheralcards_nonapple/

http://en.wikipedia.org/wiki/Z-80_SoftCard

http://www.apple2info.net/hardware/softcard/softcard.htm (With lots of docs and images and advertisements for it. They even have the CP/M disks that go with it)

Now you are making me impatient about my IIe....