where V is the price of the option as a function of stock price S and time t, r is the risk-free interest rate, and sigma is the volatility of the stock.
The key financial insight behind the equation is that one can perfectly hedge the option by buying and selling the underlying asset in just the right way and consequently “eliminate risk". This hedge, in turn, implies that there is only one right price for the option, as returned by the Black–Scholes formula.