I wondered this, because I often see it applied to other countries that don't quite fit. For example "In Britain, executive power is wielded by the head of the legislative on behalf of the monarch" or something like that... which seems like it's trying to explain Britain using a foreign system that doesn't quite work. And I see it used to describe the politics of other countries too, when it seems to best describe the USA (which has clearly delineated judicial, legislative and executive branches). So I wondered how describing governments as comprising these three parts started.
The concept was not originally an "American thing" in the sense of having being invented by American thinkers. There is also a conflation between identifying distinct powers wielded by government (one sort of action is executive, another legislative etc.) and the idea that each power should purely be wielded by totally separate institutions. The former concept still coheres with the British constitution (and parliamentary systems generally), the latter not quite.
The concept as we would recognise it was first discussed by John Locke in his Second Treatises of Government, there he outlined three "functions" of Government: the legislative, executive and federative (ability to act for the State internationally). He thought the former should be vested in a different body to the latter two, as in England (with the Parliament preforming one function and the Crown the other). Locke is talking about functions, not institutions. Hence functions can be shared between multiple bodies (parliament is composed of the King, Lords and Commons) and the same body (the King) can operate two functions. There is, therefore, no one to one correspondence between powers and institutions. Locke didn't see judicial power as a separate function but as an amalgam of legislative and executive. Secondary Source: Tuckness (2002), Locke and the Legislative.
The tripartite account of political power most familiar to us was first described by the French Enlightenment political philosopher the Baron de Montesquieu, (normally refereed to as just Montesquieu in English) in his "The Spirit of the Laws" (1748).
Both thinkers were well known among the framers of the American Constitution and were explicitly referenced by them.