"Back testing" (also called in-sample testing) is the easiest way of testing performance, but is often thought of as meaningless. An asset manager constructs a portfolio today, then based on sensible criteria they check how this portfolio would have performed against the benchmark (usually the S&P 500 Index) back to May 2007. Inevitably, because of the information that was unavailable to investors back in 2007 and the years since, the asset manager's current portfolio outperforms the index.
"Forward testing" (also called out-of-sample testing) is much more difficult to test. An asset manager builds a portfolio applying specific criteria and/or an algorithm only using information available at a starting date (say, May 2007) and pushes this portfolio forward year by year until the present. Because the testing was conducted based on the same information that was available in the past, the asset manager's forward test is done in a meaningful and honest way.