Your piano is a large investment and a dehumidifier system will help you protect it and ensure many years of trouble free playing and beautiful music.  Pianos are largely made up of wood, felt, and metal.  Extreme levels of fluctuating humidity will have damaging effects on all of these materials both in the short and long term.  When humidity levels rises, the wooden components absorb moisture from the air which causes the wood to swell and when the humidity level is low, it will cause the wood to shrink.