What does shimmy in nose landing gear mean?
the nose gear support strut contains a bearing which allows the nose wheel to swivel like a caster so the plane can turn on the ground. the nose wheel assembly itself is turned either via a hydraulic cylinder or a mechanical linkage connected to pads on the upper tips of the rudder pedals, or in some cases it freely turns on its own during the application of asymmetrical braking to the main gear. 

But whatever the details of the nosewheel design are, "shimmy" occurs when the wheel assembly wobbles rapidly back and forth (left-right-left-right) as the plane is rolling down the runway at speed. this is called castering instability and occurs when there is excessive play or looseness in the caster bearing or the support strut or the wheel bearings, or slop in the steering control circuit, or improper inflation of the nose wheel. 

The shimmy action sets up strong vibrations in the airframe that the pilot can feel and if strong enough can hear as well. Those vibratory stresses are acting to wiggle loose any bolted connections in the entire nosewheel assembly and can also seek out and activate any fatigue stress raisers present there- in addition to making the airplane difficult to accurately steer.