The escape wheel is a part of the “escapement”, which is controlled by the periodic swing of the pendulum or balance wheel. It is powered by a coiled spring or suspended weight that rotates a gear train. The escapement allows the gears to advance or "escape" a fixed amount with each swing, to move the timepiece's hands forward at a steady rate. It regulates the clock’s system, so that it doesn’t unwind uncontrollably.
The jeweled pallets and escape wheel teeth are particularly elegant in this video of a Brocot escapement in a French mantel clock.