Why did people put ashes on their gardens and is it still applicable?

Spead it on your garden good Potash!! improves the flowers and fruit.

I second that

thats what i do with mine, good for the soil and plants

What about ash from a wood/coal stove. Can anyone comment on that please.

Yes the ash from a wood coal stove is good too, the course ash is great to help lighten any clay soil when it is dug in but the clinker lumps can be removed. You can get some very hard large clinker from some stoves. I used to put those in the bin.

Coal ash is very alkaline (ph > 9) so don't use it near ericaceous plants.
While wood ash is good for most plants, it will still raise the alkalinity of your soil. The suggesstion is to use it in moderation and check your soil ph on an annual basis

Fires are good in gardens and will aid the natural breakdown of nutrients in the garden just as they do in the wild (except for coal ash).

Most of my garden's clearance is done in late October in time for November 5th. Every year I prune my bamboo grove in February. Some stems are kept for staking and the remainder are burnt and their ashes recycled beneath the living stems.