Why Beta (also written hFE) is the current gain of a bipolar junction transistor: a small base current controls a much larger collector current, and beta is the ratio of the change in collector current to the change in base current. Typical small-signal transistors have betas of roughly 50 to 300, so 1 mA of base current might support 100 mA of collector current. It is related to alpha (collector current divided by emitter current) by beta = alpha / (1 - alpha).
Watch out The choice about the frequency where gain drops to 0.707 describes a cutoff or corner frequency such as the alpha cutoff, not beta itself; breakdown voltage and switching speed are separate device ratings.
Beta = Base current boosted: collector current divided by base current.