What is the significance of the depth of an earthquake?

Earthquakes occur at depths from near the Earth's surface to about 700 km deep. (See Determining the Depth of an Earthquake.) Below that depth, rocks are too hot and ductile, so they tend to bend and flow rather than break in a brittle manner. The strength of shaking from an earthquake diminishes with increasing distance from the earthquake's source, so the strength of shaking at the surface from an earthquake that occurs at 500km deep is considerably less than if the same earthquake had occurred at 20 km depth.

Also, the depths of earthquakes gives us important information about the Earth's structure and the tectonic setting where the earthquakes are occurring. The most prominent example of this in in subduction zones, where plates are colliding and one plate is being subducted beneath another. By carefully plotting the location and depth of earthquakes associated with a subduction zone, we can see details of the zone's structure, such as how steeply it is dipping, and if the down-going plate is planar or is bending. These details are important because they give us insight into the mechanics and characteristics of the deformation in the subduction zone.

Accurately determining the depth of an earthquake is typically more challenging than determining its location, unless there happens to be a seismic station close and above the epicenter. So generally, errors on depth determinations are somewhat greater than on location determinations.