Anything done in an awkward or painful way happens uncomfortably. If the chairs in a parent-teacher conference are all sized for kindergartners, the parents and teachers will sit uncomfortably through the meeting.
If you're too close to the movie screen, you'll have to crane your neck uncomfortably, and if you have very long legs and take a lengthy airplane flight, you'll spend it bent uncomfortably into your seat. In addition to physical discomfort, there's another kind of unease that lends itself to this adverb: "They were so mad at each other that everyone sat uncomfortably, in complete silence, all the way through dinner."