I also believe it has a certain amount to do with printers, as in the ones with printing presses.
Ever look at a multi-cartridge printer? Cyan, Magenta, Yellow, Black - CMYB(k, cause B could also be Blue); in some printers, 1 for each color.
So my guess is the functionality is there for CMYK so someone who needs to make it work with a printing press can proof-check the individual colors, which each end up on their own plate - printing presses don't work like desktops, they print 1 color at a time.
At least in CMYK mode if there's a part that is just too narrow to properly end up on the plate, they can fix it ahead of time, instead of making the plate and having to scrap it later (plates ain't cheap, particularly if it's a metal plate they're using).
Off of printers though, CMYK might be supported in a particular filetype; a rough google search seems to be indicating the Tagged Image Format File (TIFF, or TIF) uses CMYK as opposed to RGB.
Assuming that's the case, some filetypes are probably preferred to printers, as opposed to others.
Jpeg on the other hand only supports the RGB style, as far as I know. So assuming you meant you went into CMYK mode, saved it, then opened the Jpeg and it went to RGB, that'd be why.
EDIT: I should clarify, I'm not a graphic designer, but I remembered this after posting:
Inks use Cyan, Magenta, Yellow, and Black to make images.
Color screens (like monitors or TV's) use Red, Green, and Blue, the primary colors of light, to make images. In the end they both look the same, but it's definitely done differently