The number of units in the underlying security needed to hedge (or which can be hedged by) a derivative is equal to the delta of the derivative.
Delta hedging is used to cover trading positions, and to arbitrage differences between the cost of the derivative and the cost of buying enough of the underlying to delta hedge it.
The delta changes with the price of the underlying, so a delta hedge must be continuously rebalanced.
As a delta hedge can be used to hedge a position in a derivative, by reversing the hedge, and combining this with cash or debt, one can replicate the cash flows of the derivative. By the law of one price the value of the derivative must be equal to the value of the portfolio that replicates it. This is used to derive the Black-Scholes formula.