If you are asking if the test explosion in North Korea physically triggered this earthquake in South Korea, you can think of it in the same terms of natural earthquake triggering. There are two physical mechanisms where earthquakes can trigger one another. One of these is static stress triggering and one is dynamic stress triggering.
Earthquakes have triggered other earthquakes across long distances (1000+ km) through dynamic stress triggering. This occurs when an already stressed fault is near the breaking point, then the surface waves of a large earthquake pass by and throw that last straw on top to make the fault rupture. Remember that there are earthquakes much, much larger than these tests that do not seem to trigger any seismicity. Some do, and you can read about those in this recent paper published in Science [summary article / Fan and Shearer, Science, 2016].
There is also static triggering which is more like a domino effect. That's where one bit of fault ruptures and puts added stress on an adjacent fault, pushing it over the brink and causing it to rupture. This is only relevant over distances of about one fault length, so over a few hundred kilometers for a big M8 or 9 but a much smaller distance (~10 kilometers) for an M6 or less.
So because the North Korean test was relatively small and about 500 km from the South Korean earthquake the strain transfer would be too localized for static triggering, and because the earthquake occurred days after the test the timing is too late for dynamic triggering.Source