Those contain the start capacitors that are needed in single-phase electric motors to get the armature spinning when the motor is first turned on. The start capacitor is connected to the AC mains and a small set of windings that accompany the main running windings in the motor. The capacitor delays the phase of the current in the start winding so that when the field winding comes on and turns the armature a little bit, the start winding then adds a slightly delayed extra kick in the same direction- an action which gets the armature turning instead of just vibrating back and forth, which is what it would do in the absence of the start winding and start capacitor.
Once the motor comes up to full speed, a switch automatically cuts out the start circuit and the motor is left running on the run winding only.
This is a task that is handled differently in different kinds of AC motors. Three-phase AC motors do not require start caps at all, since the delayed phases are furnished by the mains. This means 3-phase motors are self-starting, as are all DC motors.