I believe it is less risky to develop (e.g. you do not have to do DDR3 layout), speeds up your development (you do not need to design the core - a lot of pages of schematic and time demanding for doing layout, you just work on the simple baseboard) and it may be even cheaper for your product (you buy it form a company what sells the modules in thousands, you may never be able to get so good prices on processor or memories).
I also like, that you buy it when you need it (the module is usually most expensive part of the design, and you do not need to keep components in stock - you do not need to keep your money in it), you do not need to manufacture it (a lot of work and troubles) and if the module is damaged, you simply send it back to the manufacturer.
Many many many companies start developing their own modules or try to "copy and paste" the module on the baseboard (to have a one board solution), but after some time they realize, that it is not so simple and just go for the module solution.
By two PCBs on top of each other, you can also make the product sometime smaller.
Some companies are worried about vibrations, but many times even this is not a problem. Usually only the companies who can not use a module solution do not buy it.
PS: I do not sell the modules, so this is not an advert for it
but they really are useful. Specially, they speed up development and make it easier.