In a 10-period weighted average the most recent bar is multiplied by 10, the one before by 9, and so on, with the total divided by the sum of the weights. Unlike an EMA, data outside the window is excluded entirely.
It is used less often on its own than as a building block. The hull-moving-average is constructed from weighted averages, and some volume-sensitive averages use the same weighting idea applied to volume instead of position.
Practically the differences between SMA, EMA and WMA at the same period are small and swamped by the choice of period itself. Traders often spend far more time choosing an average type than the decision warrants; the lookback-period matters much more.
Related: simple-moving-average, exponential-moving-average, hull-moving-average, lookback-period, volume-weighted-moving-average