InfluxDB's Holt-Winters method is a powerful predictive maintenance technique that determines forecasted values by calculating an exponentially weighted average, incorporating trend and seasonality into the forecasted value. The multiplicative method uses three smoothing parameters (beta-star, gamma, and alpha) to optimize the Root Mean Square Error (RMSE), which is scale-dependent and normalized, and is optimized using the Nelder-Mead numerical method. This optimization process allows for finding good approximations of the smoothing parameters and initial values, enabling the use of Holt-Winters in forecasting time series data.