Good as long as it is from wood, not from rubbish. Watch what people put in fires when you aren't looking, and be careful what you use to light the fire. I use pine cones. Coloured paper, candles, parafin, plastics (especially blue plastic) are all possible sources of heavy metals
Wood ash contains (I think) all the minerals that were in the wood except nitrogen which volatilises. It certainly contains a lot of potassium. As ash is soluble I use it to
feed the most barren bits of scrub and grass on our
land, which are also the highest parts so hopefully the minerals will wash down. It seems to have dramatically encouraged the growth of legumes in these places which were not there before. I have also used it in the garden. It is alkaline so theoretically a substitute for lime, but I haven't noticed any big response from the vegetables.
It is not organic so I don't compost it (although organic regulations say you
should). Compost heaps lose a lot of potassium, (as do vegetable gardens) and soluble mineral fertilisers will very likely end up in the nearest
water course if not used carefully. Best around perennial vegetation in the growing season.