Wood ash is a good source of lime and potassium for your garden as well as many other trace elements that benefit plants. It is best used in moderation, scattered lightly and well mixed into your compost. Wood ash produces salts and lye and if not used sparingly can damage or kill your plants - when composted much of the salts and lye is depleted.
Ashes from hardwoods, such as oak ,maple, walnut are best, the nutrients and minerals in wood ash from hardwoods is much higher. Softwoods such as pine contain less nutrients and minerals.
Wood ash is also helpful to control some pests. The salt in the wood ash kills snails, slugs and deters some other soft bodied invertebrates.