beta = Cov(asset, market) / Var(market) - the slope of a regression of asset returns on market returns.
A beta of 1.5 means the asset has historically moved 1.5% for each 1% market move.
The limitations. Beta is estimated with substantial error and is unstable over time. It captures only linear co-movement with one factor, and it typically rises in crashes - so a hedge sized on calm-period beta under-hedges exactly when it matters.
Market-neutral portfolios target zero beta, which is a much weaker condition than being risk-free.