Wood ash is the residue powder left after the combustion of wood, such as burning wood in a home fireplace or an industrial power plant. It is used traditionally by gardeners as a good source of potash.
Fertilizers Wood ash can be used as an organic fertilizer used to enrich agricultural soil nutrition. In this role, wood ash serves a source of potassium and calcium carbonate, the latter acting as a liming agent to neutralize acidic soils.
Wood ash can also be used as an amendment for organic hydroponic solutions, generally replacing inorganic compounds containing calcium, potassium, magnesium and phosphorus.
Composts Wood ash is commonly disposed of in landfills, but with rising disposal costs, ecologically friendly alternatives, such as serving as compost for agricultural and forestry applications, are becoming more popular. Because wood ash has a high char content, it can be used as an odor control agent, especially in composting operations.
Pottery Wood ash has a very long history of being used in ceramic glazes, particularly in the Chinese, Japanese and Korean traditions, though now used by many craft potters. It acts as a flux, reducing the melting point of the glaze.
Soaps Potassium hydroxide can be made directly from wood ash and in this form, is known as caustic potash or lye. Because of this property, wood ash has also traditionally been used to make wood-ash soap.
Bio-leaching The ectomycorrhizal fungi Suillus granulatus and Paxillus involutus can release elements from wood ash
More info here: https://permies.com/t/6013/wood-ash