They are traits, if you look at them the DoW traits convert melee stats into magic stats and the DoM traits turn magic stats into melee stats...
Uses for this could be something like, my main is gladiator but i want abilities from thaum and conjurer without having to reallocate my points every time i switch jobs.
Or for those really hardcore people they can level a mage job to the point where it can earn marks and then buy conversions for mage stats into melee stats, since stat point costs increase at 40 (and maybe at 80?) this would allow people to get 5-10 stats without having to spend 10-20 stat points to get them.
FFXI: Ferth - Cerbereus Nee Hades Nee Leviathan.