Large earthquakes are usually connected with plate boundaries. Earthquakes happen often but most are too small for us to notice. Seismometers record earth movements.
An earthquake is a sudden shockwave caused by rocks being under stress from the movements of plates at plate boundaries. Eventually the stress in the rock builds up enough to deform and reach breaking point. At that point, the stored up energy is released in the form of shockwaves.
In the past, the Richter scale was used to measure the power of earthquakes. Earthquakes are now measured using the Moment Magnitude Scale (or simply Magnitude scale). This measures the size of the seismic waves during the earthquake. Each step in the scale is ten times greater than the previous number. This is a logarithmic scale.
The amount of damage caused by an earthquake is measured by the Mercalli Scale. This is a measure of intensity, and changes according to which area you are measuring - damage nearer the epicentre would usually be greater than further away.