AUI – Attachment User Interface – provides the ability to connect – through the use of a AUI transcevier – a dissimilar transport media to the specific device. A AUI transceiver in conjuction with the AUI port provides the translations required to enable things to work and communicate..
A simple example would be that you have a fiber segement that you wish to attach to your device. However your device does not provide a fiber port for connection, but does provide an AUI port. Then through the use of a Fiber Transceiver it could be attached to the AUI port of the device.
Caution there are limitations and restrictions and variations of this usage and the complete information regarding the port usage is dependent on the manufacturer of the specific device instructions.
The basic difference is just that an AUI is older and more versatile; same performance, however. AUI ports originated back in the days of ThickEthernet but over time, other media standards developed and you can now get transceivers for ThickEthernet, ThinEthernet, 10BaseT(RJ-45) and fiber. For a non-modular router like the Cisco 2500 series, the AUI architecture provided the versatility that is now provided by plug-in modules within the router (or switch) itself.
AUI seems to be slowly dying out in current generation routers and switches but I think it still has a lot of life left in legacy equipment.