Almost every modern functioning state seems to have a similar blueprint.
There are 3 powers: parliament, government and judiciary. Parliament is elected and gives laws, government voted by parliament and provides administrations while the judiciary is professionalized/meritocratic applying the law. Other common things: members of parliaments are voted from political parties, there is a high/supreme court (or constitutional court), attorney general and others.
The question is who and when invented this blueprint? And how come is this model so ubiquitous?
While I can't speak for most of the things mentioned, Separation of Powers is widely believed to have originated from John Locke's Second Treatise of Government and later Montesquieu's The Spirit of the Laws, the general idea they both had was that separation would prevent tyranny. As far I'm aware the first practical application of this principle was the US Constitution written up in 1787.
I'd also like to clarify what 'Government' refers to, government is not voted in by Parliament as a Parliament is a Legislature which is one of 3 (the others are Executive and Judiciary) branches which collectively form a Government.
It's also worth noting that generally there's 2 types of systems out there, a parliamentary one which typically fuses some or all of the branches such as the UK, or the presidential one like the US which strictly separates the powers. Parliamentary is typically prevalent in constitutional monarchies (where a monarch is Head of State, a Prime Minister is technically in charge in all but name), while presidential ones are in republics (where a President is Head of State) which typically form where monarchs were ousted (France, Germany) or there's the US which broke away from the British Empire and formed one anyway. There's also rare exceptions like Israel where they have both a Prime Minister and a President, but they work just like constitutional monarchies so the President is simply ceremonial.