This is generally done to obtain a more robust statistic, and the extreme values are considered outliers.
Given an estimator, the x% trimmed version is obtained by discarding the x% lowest or highest observations or on both end: it is a statistic on the middle of the data.
In some cases a trimmed estimator discards a fixed number of points (such as maximum and minimum) instead of a percentage.
However, if the distribution has skew, trimmed estimators will generally be biased and require adjustment.
(using the error function) makes it an unbiased, consistent estimator for the population standard deviation if the data follow a normal distribution.