On the Amiga 500 there is an expansion port
How did the expansion port work?
That expansion port exposes all the signals from the 68000 CPU, plus some other Amiga specific signals, such as the color CLK, ROM and RAM select signals, along with voltage supply lines, etc. It is documented in the schematic, page F-9 of the User's Manual.
It worked by removing its trap door, and plugging in a compatible device with the Amiga switched off. When switched back on, the device starts operating and depending on whether it has a boot ROM, it may override the normal Amiga boot procedure, or simply sits there in the bus waiting for a driver that had to be loaded during the Amiga OS initialization process so it can answer requests from the OS and applications.
You can put it any hardware device designed to work with the 68000 bus and the Amiga 500: from an IDE interface to a complex device. Or you can completely override the internal 68000 and provide your own CPU, as long as it is binary compatible with the 68000 and generates the same control signals (e.g. what an accelerator board does)
Common expansions for the A500 included: Action Replay, SCSI hard disks and CPU accelerators. The Amiga Hardware Database lists many expansion devices, many of them usable with the A500 through its expansion port (along with other devices that used the parallel port or the memory expansion port) http://amiga.resource.cx/expansion.html
In addition to mcleod_ideafix' answer above: Commodore also made a CD-ROM drive that plugged in the slot (unfortunately without a feed-through slot on the other side): the A570 turned the Amiga 500 into a CDTV.
Unfortunately, the A570 was released after the A500 was discontinued and replaced with the A600, it had a caddy (not a tray) and it ran at single-speed. So it wasn't very popular.
In short, the Amiga 500 expansion port was an exact electrical equivalent of the expansion port of Amiga 1000, and very similar to the Zorro II card slots of the Amiga 2000 and above.
The Zorro II card slots of the Amiga 2000 and greater models had 14 extra pins compared to the Amiga 500/1000 expansion port.
When you remove the expansion port cover on an Amiga 500, the large chip you see above the card edge connector is the actual 68000 processor - so you can see that the expansion port provides very direct connectivity to the processor.
Another fairly common expansion, which was not an accelerator, RAM, or 68k compatible, was the PC compatibility card containing an x86 compatible CPU. In fact, one of the first hyped Amiga sidecar expansions was the original Sidecar.