'showstopper' is a compound formed in modern English from the noun 'show' + agent noun 'stopper' (mid-20th century usage in theatre), where 'show' referred to a public entertainment and 'stopper' meant 'one that stops'.

'showstopper' developed as theatrical slang in American and British English to describe a number that figuratively 'stops' the show by eliciting prolonged applause; it was formed by compounding 'show' and 'stopper'. 'Show' itself goes back through Middle English to Old English 'sceawian'/'sceawung' (see/view), while 'stopper' derives from 'stop' + '-er' (Old English/Proto-Germanic roots for 'stop').

Initially it meant 'a performance item that stops the show (by applause)' in theatre contexts; over time it broadened to mean any spectacular highlight and later also gained a nearly opposite informal sense in business/tech as 'a critical obstacle or deal-breaker'.