Hi Nina and Fung F.C.,
The importance of the value/growth distinction comes from the research done by Eugene Fama (who won a Nobel prize for it) and Dan French. The Fama-French three-factor model separated excess stock returns (actual returns minus the risk-free rate) into the small-stock factor (called SMB for "small minus big") and the value factor (called HML for "high minus low," referring to those stocks with the highest ratio of book value to market value compared to those with the lowest ratio) plus the market factor (basically everything not explained by SMB and HML). Dan French's web site (http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html)shows the monthly values from July 1926 through October 2015, and over that entire period the value factor has averaged 4.62% per year, meaning that value stocks have outperformed growth stocks by that amount on average. The small-stock factor has averaged just 2.56%, so the value factor has been much more important than the small-stock factor.
Lots of additional research has focused on (1) other factors that appear to be important, as well as (2) other ways of identifying "value" versus "growth" stocks. Basically, however, the way that "value" and "growth" are defined for the purpose of this research means that we are not looking at things like a low-valuation stock with no/low growth or a high-valuation stock with high growth or a high-valuation stock with no/low growth or a low-valuation stock with high growth.
--Brad