Premiere
The noun premiere (sometimes referred to as a world premiere in 20th century parlance), is broadly defined as "the first public performance of a play or any other type of entertainment"[1].
The Merriam-Webster online dictionary[2], adds the following uses of the term as a verb: 1 : to have a first public performance. 2 : to appear for the first time as a star performer. transitive verb. : to give a first public performance of. (i.e "to premiere the play")
The term world premiere
While premiere has come to be used of any production (even second or subsequent new productions of the same play), the phrase world premiere strictly speaking refers specifically to the very first regular performance of a theatrical event of any kind, anywhere in the world.
However, this term has in many instances been misapplied in the case of many South African theatrical productions over the years, very often being used to refer only to the first performance outside the country, instead of the first performance ever - inside or outside the country.
To take but one example: to this day the Royal Court Theatre in London lists their 1974 production of Athol Fugard's Statements After an Arrest Under the Immorality Act as the World premiere" of the play, despite the fact that the play had been commissioned by, and had its very first run at, the Space Theatre in Cape Town in 1972, with author Athol Fugard and Yvonne Bryceland in the leading roles.
While clearly a marketing strategy nowadays, this usage to a great extent also derived from the circumstances prevalent in the colonial and Apartheid eras, and probably encompasses something of what the Australians refer to as the colonial "cultural cringe", an attitude whereby any artistic work is only considered notable if it is recognized in Europe or America.
This particular use of the term is less prevalent today though.
Sources
Merriam-Webster online dictionary[3]
Cambridge Dictionary online[4]