Ten kilometers is a "fixed depth". Sometimes data are too poor to compute a reliable depth for an earthquake. In such cases, the depth is assigned to be 10 km. Why that number? In many areas around the world, reliable depths tend to average 10 km or close to it. For example, if we made a histogram of the reliable depths in such an area, we'd expect to see a peak around 10 km. So if we don't know the depth, 10 km is a reasonable guess. The USGS used to use 33 km, but increased understanding indicates that 10 km is more likely.
Some areas, like subduction zones, are known to have many earthquakes much deeper than 10 km. In those areas, a deeper fixed depth would probably be appropriate. The most common reason for having to fix the depth is that the earthquake occurred too far from the nearest seismic station. A useful rule of thumb is that a reliable depth requires that the distance from the epicenter to the nearest station must be less than the depth of the earthquake.
Modern computational and theoretical advances can now produce reliable depths at greater distances from the nearest station, so the rule of thumb does not always apply. However, the rule of thumb does illustrate one conclusion: fixed depths are more common for shallow earthquakes than for deep ones.