The regression takes a portfolio's excess returns and fits them on three series: the market premium, small minus big, and high minus low book-to-market. The intercept is what is left unexplained, and it is that intercept, not raw outperformance, that gets called alpha in academic work.
The practical effect was to shrink a lot of claimed skill. A manager beating the index by 3% a year while loading on small and cheap stocks often showed an intercept close to zero, meaning the return was replicable with a rules-based portfolio at a fraction of the fee.
Later extensions added momentum and, in a five-factor version, profitability and investment terms. Each addition explains more, which also means each addition raises the bar a manager must clear. See profitability-factor.
Related: alpha, capital-asset-pricing-model, value-factor, size-factor, profitability-factor, factor-investing