In the context of investing, alpha is excess returns earned by an investment, above the benchmark.
For example, an active portfolio of large-cap US stocks may use the S&P 500 as a benchmark. If the portfolio outperforms the S&P 500 over a period, then the portfolio achieved a positive alpha. Portfolio managers may be judged by the alpha they generate.
Bankrate's article: What is alpha?
Investopedia article on alpha