They have special Exif data.
I've been toying around with the DSi and trying to get it to display pictures I put on from my computer. I used PhotoME to view and edit some Exif data. I found out that the DSi stores some data in the Exif data that pertains to the image. In PhotoME it's displayed as the Binary Data under Manufacturer Notes.
So far I've only been able to manage copying an image on the SD card without use of the DSi. But that's only because I didn't have to change any Exif Data. The DSi stores a list of images on the SD card, located in "private/ds/app/484E494A/pit.bin" if you delete that, then the DSi recreates it by scanning the images on the card and adds them all to the list. If you copy a picture (and rename it to the appropriate name, e.g. HNI_0017 would become HNI_0018), the DSi won't recognize it's there unless you delete the pit.bin file.
Editing an image, though, requires that the exif data under "manufacturer's notes" somehow conforms to the picture. I haven't any experience cracking codes, so this is as far as I got. I imagine that this is the only thing that's holding up people from putting images on the DSi. If you "Import/Export -> Export EXIF data" from a working DSi image and "Import/Export -> Import EXIF data" to an edited image, it won't work. It comes up saying "Cannot Display Image." Although it at least recognizes that something's there. It just won't display it.
This is what I've found out through exploring for a half hour or so.
Once someone cracks the code for the "Manufacturer Notes" that might be all that's preventing the DSi from showing the picture. Of course, there also might be more protection behind it. I haven't really done any research into what has and hasn't been done for this. So if this is already widely-known, sorry for wasting your tine.