The recursion is simple: new estimate = lambda x old estimate + (1 - lambda) x new observation. With lambda = 0.94, the standard RiskMetrics choice for daily variance, the most recent day gets 6% of the weight and data from 60 days ago contributes under 0.2%.
Compared with a simple rolling-window, EWMA avoids the ghost effect where a single huge day drops out of the window and the estimate falls off a cliff for no reason. Weights decline smoothly instead.
The effective memory is roughly 1/(1 - lambda) observations, so 0.94 behaves like a 17-day window and 0.97 like a 33-day one. Choosing lambda is therefore the same decision as choosing a window length, with the same parameter-sensitivity obligations.
Related: garch, realised-volatility, rolling-window, volatility-clustering