When it first appeared in the U.S. in the early 1800s, discombobulate was just a playful, rootless coinage conveying a sense of confusion. It was probably inspired by similar words like discomfit and discompose, but the -bobulate part has no etymological origin. It is this nonsense quality that gives the word its meaning—i.e., to throw into a state of confusion. To be discombobulated is to be thoroughly befuddled.
Discombobulate is still a light word and might be out of place in more formal contexts, but it does turn up fairly often in edited publications—for example:
But the discombobulated process that preceded it has scared the markets into inertia and lethargy. [Wall Street Journal]
Therrien’s giant table and chairs leave you discombobulated and delighted. [Guardian]
Rarely does a federal agency manage to discombobulate the press as thoroughly as Elections Canada did with the issuing of a single report on Wednesday. [National Post]
Weaver … uses a three-quarter, cross-body release that discombobulates hitters from both sides of the plate. [Sports Illustrated]