Post-neoclassical endogenous growth theory is a phrase made famous by Gordon Brown, then the UK Labour Party's shadow chancellor, in a 1994 speech; it was widely mocked as jargon. It refers to endogenous growth theory, explained in full on that page.
That theory, developed by Paul Romer and others, holds that long-run growth comes from ideas, human capital and research and development that policy can influence, rather than only from outside forces as in neoclassical growth models.