The exponent associated with inverse distance weights determines how quickly the influence of neighbouring points drops off. With inverse distance, when trying to estimate an elevation (e.g.) at an unknown location, the weight (or significance) the interpolating routine gives to the elevation value at each known (sampled) location decays rapidly as the distance between the known and unknown points increases.  How rapidly this occurs can be adjusted to best fit your real world situation by adjusting the value of the exponent.  This graph illustrates the influence on inverse distance weighting for exponents 1 - 6. Note that you can use an exponent of less than 1, although that would give points further away a greater influence than nearer points!