Our planet's seemingly stable surface is made up of enormous pieces of rock that are slowly but constantly moving. Those pieces continually collide with and rub against one another, and sometimes their edges abruptly crack or slip and suddenly release huge amounts of pent-up energy. These unsettling events are called earthquakes, and small ones happen across the planet every day, without people even noticing. But every so often, a big earthquake occurs, and when that happens, the pulses of energy it releases, called seismic waves, can wreak almost unfathomable destruction and kill and injure many thousands of people. 
Earthquakes happen when the ground literally shakes. Usually earthquakes are due to shifting Tectonic plate and tension between plates that is suddenly and explosively released. Earthquakes can cause terrible damage and terrible loss of life. Earthquakes under the Sea or Ocean can cause Tsunami so people who feel an earthquake near the coast should evacuate to high ground fast.
Technically, an earthquake is a vibration that travels through the Earth's crust. Quakes can be caused by a variety of things, including meteor impacts and volcanic eruptions, and even sometimes man-made events like mine collapses and underground nuclear tests.