Elastic rebound is what happens to the crustal material on either side of a fault during an earthquake. The idea is that a fault is stuck until the strain accumulated in the rock on either side of the fault has overcome the friction making it stick. The rock becomes distorted, or bent, but holds its position until the earthquake occurs, and the rock snaps back into an unstrained position, releasing energy that produces seismic waves.
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As tectonic plates are slowly moving, their edges are locked in place, causing bending of the crust along the plate edges. When the force trying to make the edges slip overcomes the friction making them stick, there is an earthquake. The bending and subsequent "catching up" of the crust is called "elastic rebound."