In neoclassical growth models, growth is exogenous. That is, there is some variable - usually "technology" - that grows by assumption. Therefore, neoclassical growth models are able to describe how an economy grows, but now why it grows.
Endogenous growth theory tries to overcome this shortcoming by making growth an endogenous variable (hence the name). Several competing models have been developed by various authors. Crucial importance is usually given to the "production" of new technologies and human capital.
In contrast to the older neoclassical growth theory, endogenous growth theory argues that policy measures can have an impact on the long-run growth rate of an economy. Subsidies on research and development or education are generally thought to increase the growth rate - a result that is very much in line with university professors' personal preferences.