Natural beech wood is a beech wood, that is able to replenish and sustain itself on its own.
Beech is a valued timber, but most beech woods require human intervention to replace old trees, since the young trees are not able to survive at all, or at a rate that sustains the beech population over time. There can be various reasons for this condition. Heavy forest floor coverage of other plants in the spring, shadowing the young beech-shoots, is a common cause. Abundance of nutrient-rich soils will also be difficult to handle for beech woods in the long run.
A natural beech wood has beech trees of all ages, including fallen and dead trees. Other tree species might be mixed in, but not to a degree that threatens the dominant beech.
The term is also used for other tree species, such as 'natural oak wood', 'natural birch wood', etc..