A rash was any change to an individual's skin which affected its appearance or texture. A rash could often be the symptom of an illness.
In 2370, Beverly Crusher initially believed that a mark on Deanna Troi's shoulder was a rash from the coil brace Data had stabbed her with; it ultimately turned out to be an interphasic organism. (TNG: "Phantasms")
In 2371, Ishka suffered a slight rash due to her skin being a little sensitive to clothing. This therefore did not constitute a medical ground for the FCA to drop their charges against her for earning profit. (DS9: "Family Business")
Soon after, while attempting to woo Captain Kathryn Janeway, Q placed a romantic bed in her quarters, complete with satin bedsheets. Janeway, however, was not amused and ordered him to remove the bed, but Q refused, stating "I have no intention of getting between those Starfleet issue sheets. They give me a terrible rash." Janeway replied that it wouldn't matter, since he wouldn't be getting in the bed. (VOY: "The Q and the Grey")
In 2374, while on board the USS Prometheus, The Doctor claimed that one possible symptom of the Terothka virus was a rash. He said that some persons found the rash worse than the stomach cramps that could also result from the virus. (VOY: "Message in a Bottle")
In 2378, Tuvok devolved a cutaneous eruption which The Doctor informed Neelix of, breaching doctor-patient confidentiality. Later that year, believing his destruction to be inevitable, The Doctor confessed this to Tuvok. As The Doctor survived, this incident became an embarrassment. (VOY: "Renaissance Man")