A weighted average or weighted mean is an average which is obtained by combining different numbers (e.g. prices or index numbers) according to the relative importance of each.
A weighted average or mean is one where each item being averaged is multiplied by a number (weight) based on the item's relative importance, rather than treating each item equally. The weights or weightings are the equivalent of having that many similar items with the same value involved in the average. The result is summed and the total is divided by the sum of the weights.
An arithmetic average can be considered a special case where all values are valued (weighted) equally.