late Middle English (in the sense 'emit as vapour through the surface'): from French transpirer or medieval Latin transpirare, from Latin trans- 'through' + spirare 'breathe'. Sense 1 (mid 18th century) is a figurative use comparable with ‘leak out’
The standard general sense of transpire is ‘come to be known’ (as in it transpired that millions of dollars of debt had been hidden in a complex web of transactions). From this, a looser sense has developed, meaning ‘happen or occur’ (I’m going to find out exactly what transpired). This looser sense, first recorded in US English towards the end of the 18th century, is criticized for being jargon, an unnecessarily long word used where occur and happen would do just as well. The newer sense is very common, however, accounting for around half of the citations for transpire in the Oxford English Corpus.