The harmonic mean of x1,...,xn is
n / (1/x1 + ... + 1/xn)
As the name implies, it's a mean (between the smallest and largest values).
An extension to the AM-GM inequality relates the harmonic mean to its more famous cousins, the geometric mean and the arithmetic mean.
The word "harmonic" is often used when inverses are involved; doubtless the harmonic mean has (Pythagorean, and therefore mystical) connections to musical harmony and pleasing intervals.