Backed out of the market price by root finding, usually Newton-Raphson using vega as the derivative.
Why traders quote in vol. Option prices move mechanically as the underlying moves; volatility is far more stable, so a vol quote isolates what is actually being traded and stays comparable across strikes and expiries.
Implied usually exceeds subsequently realised volatility - the variance risk premium, compensation for bearing volatility risk. That gap is why systematic option selling has historically paid, right up until it catastrophically has not.