MRW growth theory's name is from Mankiw, Romer, and Weil, three economists who wrote a paper on economic growth around 1992. It uses a mathematical model to estimate economic growth, based on past data from a group of countries. Economic growth is estimated based on national savings, education, and population growth.
The paper has been heavily criticised: it uses a flawed theoretical model, it examines only a few of the causes of growth, its empirical estimation could be better, its data is imperfect. Even its supporters recognise its limitations.
Yes; and the paper is still an example of how economic research should be. It is scientific in its process: it proposes a model to describe existing data, fits the data sufficiently given the state of empirical techniques at the time, expands the theoretical model to a new setting, and produces predictions from the expanded model which have proved substantially correct. Its predictions are in perhaps the most important area of macroeconomics. Numerous other researchers have published minor or substantial modifications to the theory, and it has given momentum to studies of improved empirical estimation techniques not solely applicable in growth theory but throughout social sciences.
All in all, fab.