What reaction takes place when palm-oil is added to potash and foam are observed?

Palm oil is a fat or oil, which is an ester. Potash (from burnt plant ash) contains potassium carbonate, which is alkaline.

When an oil is boiled with an alkali, it breaks down into glycerol and the potassium salt of fatty acids. That salt is soap, and it makes foam. This reaction is called saponification.

Neutralisation is acid with base. Esterification makes an ester from an acid and alcohol, which is the reverse of this. Salting-out is adding salt to separate soap.