late Middle English (in the sense 'emit as vapor through the surface'): from French transpirer or medieval Latin transpirare, from Latin trans- 'through' + spirare 'breathe'. The sense 'be revealed' (mid 18th century) is a figurative use comparable with 'leak out'
The common use of transpire to mean ‘occur, happen’ (I’m going to find out exactly what transpired) is a loose extension of an earlier meaning, ‘come to be known’ (it transpired that Mark had been baptized a Catholic). This loose sense of ‘happen,’ which is now more common in American usage than the sense of ‘come to be known,’ was first recorded in US English toward the end of the 18th century and has been listed in US dictionaries from the 19th century. It is often criticized as jargon, an unnecessarily long word used where occur or happen would do just as well.