A piano is made from natural materials - wood, felt, leather, and wool. All of these materials absorb moisture from the air. When the air gets more humid, the materials absorb more moisture. Then they give it up again when the air gets dryer.
The moisture content of the natural materials affects their dimensions. This is especially true of the piano's soundboard. The soundboard is a thin sheet of wood, about 3/8 inch thick, and has a bowed or crowned shape. Blocks of wood called bridges are positioned against the soundboard and press firmly against the strings.
As the relative humidity of the air increases, the soundboard's moisture content increases along with it -- this swells the wood. The soundboard's crown increases with the swelling and intensifies the pressure against the strings. This raises the pitch of the piano. The opposite happens when the relative humidity decreases.
High humidity also causes the wooden parts of the piano's action to swell. This can lead to sticking keys and a sluggish, unresponsive action. As the felts on the hammers swell from the humidity, the sound of the piano can become soft and muffled.
Humidity Can Damage a Piano
The repeated changes in the dimensions of the wood as the relative humidity rises and falls can eventually damage the piano. The sound board can crack and glue joints can separate. As the pin block repeatedly swells and contracts, the tuning pins that hold the strings can eventually loosen and the piano will no longer hold tune.