Charcoal is wood that has been burned without sufficient oxygen. All the water and volatiles have burned off. Which means if you burn it again in sufficient oxygen it burns much hotter then the wood it was made from. Since it burns so much hotter (especially if you force air into it with bellows or a leaf blower) it can be used to smelt and work iron and other metals. It can also be used to make gun powder and as a filter since its full of pores where other substances can be absorbed. In gunpowder those pores get filled with potassium nitrate (salt petre) and sulfer. In water filtration the pores absorb the pollutants in the water (or air in the case of gas masks). During World War I the British filled their gas masks with coconut charcoal, the US used fruit pit to make their charcoal. Charcoal filters are a good place to start, but aren't completely effective for water treatment. But filtering through layers of sand and fine charcoal does filter out the gross impurities. Good charcoal should be completely black, if its brown then it hasn't been burned long enough and won't burn very hot or absorb very much.

Ashes are the product of complete combustion either of wood or later charcoal. Ashes are the very fine, soft, grey stuff. Ashes can be soaked in water to produce potash or potassium carbonate solution. If you have limestone near you, you can burn it to produce quicklime, which can then be mixed with water to form a calcium hydroxide solution. Mixing a calcium hydroxide solution with a potash (potassium carbonate solution) makes a potassium hydroxide solution and precipitate of calcium carbonate. Potassium hydroxide is a strong base and will corrode metal and pretty much anything else. It can used to make soap by mixing it with fat. If you spill it or especially if you get it on you use a weak acid like vinegar or lemon juice to neutralize it. Calcium carbonate is baking soda, which you can go on to use as a leavening agent for quick breads.