A stone is more dense than water. That is, if you compare the mass of a stone to the mass of the same volume of water, the stone’s mass will be greater. Therefore its weight will also be greater, so W_stone – W_water will be positive, and there will be a downward net force. Therefore the stone will move downward through the water until it rests on the bottom.

Wood, on the other hand, is less dense than water. If the wood is pushed under water W_wood – W_water will be negative. There will be an upward force on the wood and it will rise. How far will it rise? As some of the wood rises above the level of the water the volume and the mass, and therefore the weight, of the water displaced will be reduced. When the weight of the wood and the weight of the water displaced are equal, the net force on the wood will be zero and it will no longer move.