You need to understand how the Wii's content is managed.
The Wii has "slots" where you can install system files to it (a slot is only a folder with a number, from 1 to 257).
each IOS that nintendo is making is installed in one of these slots.
For example IOS37 means that the slot (folder) numbered 37 contains an IOS (system file/program/functions) used by games to communicate with the console's hardware.
Each application or games you run on your Wii load one of the IOS (and only one) to be able to interact with wiimotes, USB, etc.
cIOS 249 means : custom IOS installed in slot 249
It doesn't tell which IOS content is installed, it only tells you that "slot 249 is used and it contains something".
it can contains anything, what you want to know is the content of that slot, or else it will have no useful information.
cIOS d2x : This is the content.
cIOS is a modified, patched, IOS, based on one of the IOS from Nintendo.
Each game requires specific functions, like access to USB (for microphone, or Wiispeak for example), and this function is only available in a specific IOS by nintendo (USB is in the IOS installed in slot 58).
What hackers are doing is : Take IOS 58 as base, modify that file to add more functions (like Reading games from USB instead of Disc).
The resulted/modified IOS is called cIOS (custom IOS, patched IOS, modified IOS, what you want) and it must be installed somewhere on your Wii for games to use that patched IOS instead of the original IOS.
Nintendo released only few IOS, installed in slot 1 to 80.
As there are 257 available slot, hackers started to install the patched IOS in slot near the end of the available space, and 249 was chosen randomly.
There are different patched IOS type used by USBLoaders:
Hermes, Waninkoko, d2x, (There's also on-the-fly temporary patch solution (patchmii, ahbprot) but I'm talking only about permanent installed solution for now).
They are patches created by different hackers.
d2x being the newest type (it's an update to waninkoko cIOS).
As the patched IOS had multiple releases, bug fixes, features (support for FAT32, support for Big HDD, etc.), there are multiple released versions of a same cIOS type. for example cIOS rev17, cIOS rev21, d2x v8, d2x v10
How to interpret this :
cIOS 249 D2x v10 [56] : Slot 249 contains a patched IOS of type "d2x version 10" based on the original IOS installed in the slot 56. It contains all the functions the IOS 56 can do, plus an additional SD/USB access for USBLoaders.
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Now about DIOS MIOS.
The Wii can play GameCube games by using a specific IOS used for GameCube emulation. (you see, what I explained above, each IOS has their own purpose)
That IOS is installed in the slot 257 (called the MIOS slot).
DIOS MIOS is a modified/created MIOS.
As your Wii has only one MIOS slot, when you install a MIOS, it replaced the current MIOS with the new one. to change the MIOS, just install another one and it will overwrite the previous one.
there are different MIOS :
MIOS : official from Nintendo, play official game disc
cMIOS : from wiigator, let you play backup from burned disc
DIOS MIOS Lite : From Crediar, let you play backup from SD card
DIOS MIOS : From Crediar, let you play backup from USB
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To play GameCube games, you don't need cIOS 249 at all.
GameCube use the MIOS slot, not the slot249.
Slot249 may be used by some Wad Managers (homebrew to install content on the wii) to get access to the internal Wii's NAND and install DIOS MIOS in slot MIOS.
But it's not required as some manager don't even need a patched IOS to access the Wii's internal memory.