Crust refers to the outermost shell of a terrestrial body. Earth's crust is our planet's outermost layer, the place where life exists. The continental crust is the reason land life could evolve from marine life. The significance of the crust lies in this very fact (supporting life), and since Earth is the only known planet with life on it, Earth's crust is responsible for supporting the only place where life exists in our universe.
Earth's crust was formed after the core and mantle were formed from hot gases and dense matter (i.e., the initial planetary stage). When cooling took place, the core solidified, followed by the mantle. During this phase, metals that remained liquid in upper reaches of the mantle solidified and formed the initial brittle outer crust.
Over time, this layer thickened and is now about 40 km in thickness (although the thickness varies from place to place). The crust formation (and destruction) is a continuous activity and is governed by tectonic forces that continually tear it apart and form young crust.