the term comes from the CAPM (Capital Asset Pricing Model), in short
r = alpha + beta * (r_m - r_f)
Where r is the fund's return, r_m is market return, r_f is risk-free deposit rate. Theory says that alpha=r_f, and its easy to increase your return by borrowing on margin which changes beta, or investing into more risky stocks. However, it is difficult to produce alpha and thats where the hedge fund pitch comes from. They will also claim that they have small or zero beta, meaning their return does not depend on where the market goes.
I am personally of the opinion that wherever such claim is justified by past performance data, you can shove them a 100K

, should be fine unless they are conmen that is. Keep in mind that none of the top-quality funds are open to new investors. Plus, if you do not satisfy the high-net-worth individual requirements (like some here insinuate) and they are willing to look the other way, they most likely are con men.
But the real issue is whether you can figure out, if its not the SP500 that drives their return then what? Some have no original ideas any more than the Vanguard index fund, just doing the bread-and-butter hedgefund trades: the yield-curve carry, the yen/dollar carry, some short S&P puts, some short variance, but figuring out what exactly they do is probably hard.
K