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USGS
Why Do Earthquakes Happen?
When the giant blocks of rock which, because of plate tectonics, move in different directions, they are bound to bump into each other. These blocks of rock come in contact at faults. Sometimes they slide smoothly past each other along a fault. But other times the blocks of rock get stuck - the rough surfaces of rock snag, preventing movement along the fault. That might lead to an earthquake.
There might be no movement along a fault for a long time if the blocks of rock are hitched together. However, plate tectonic force continues to push the rocks so the energy continues to grow. The energy builds over decades, centuries, and sometimes even over millennia.
Eventually the energy is released as an earthquake when the force is large enough. The rock breaks, often very deep underground, and moves into a new position. Vibrations called seismic waves travel outward in all directions from the point where the energy was released, known as the focus. Like a stone tossed into a pond that sends concentric circles of ripples outward, the seismic waves radiate from the focus of the earthquake. These seismic waves are what people on the surface of the Earth feel when they are in an earthquake.
There are different types of seismic waves. Some rumble the ground surface for hundreds or even more than a thousand miles. Other types of seismic waves travel through the planet. While people in Cuba can't feel an earthquake that shakes Japan, instruments called seismographs can record the seismic waves that have traveled through the planet.
Sometimes small earthquakes are caused when fluids are pumped underground.