Earthquakes are produced by the release of stress on discrete breaking planes of the earth's crust. When that stress is released in large earthquakes the deformation can be obsered and measured. This gives us an idea of the size of the fault and its geometry. Often, large earthquakes occur on a faults that are not very well known. And looking at the patternof deformation is one of the ways we can have an insight on their characteristics.
Volcanoes deform constantly.
But also when a volcano is in relative quiescence, we can monitor the injection of magma at depth because that deformation too reaches the surface. Again, this tool allows us to understand better how volcano work. In all places where there is an underground resource, people have dug to get at it and extracted it. But often the ground settles and deforms from this human induced activity. InSAR allows us to monitor water and oil pumping or injection cycle over the seasons and to measure the behaviour over the years.