Alpha is a measure of return.
It represents the value a manager adds to the performance of the portfolio over the market. Alpha purposely does not take into account pure market performance or the particular risk level of the strategy. Rather, it offers an indicator of the manager's skill due to his/her ability to provide value-added returns to the strategy for clients -- rather than, for example, simply participating in a bull market.
For example, if a fund had an alpha of 1.0 during a given month, it would have produced a return during that month that was one percentage point higher than the benchmark Treasury. Alpha can also be used as a measure of residual risk, relative to the market in which a fund participates.