Is wood a renewable or a non-renewable resource?

Renewable is the key word here. Resources like gold, silver, oil, coal are not renewable, at least on a time scale we could recognize. When you use up a non-renewable resource, it's gone.

So some forests are renewable, that is, trees can be replanted and grown to maturity in place of those that are cut down.

Others are not renewable, like rain forests that have taken thousands of years to grow.

If you cut one tree down, you can plant one in its place. In forestry, this is called rotation. Many forest lands in, for example, the south of the USA, are on a 35 year rotation. The timber will be selectively harvested up to 35 years of age, then cut and replanted. This timber is a renewable resource, also called plantation forests, which are planted and then cut down to make paper. It is sometimes called a sustainable resource, so long as we keep planting and growing trees at the same rate or better as we cut them down.

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Technically a tree is a renewable resource, as you can replace what you use in about 20 years depending on the species of tree. However, when companies cut down entire forests of trees, much biodiversity is lost and it is too hard to replace what was destroyed.

Unfortunately, trees are often consumed in a non-renewable fashion. History is filled with stories of trees being harvested in a non-renewable fashion, leaving what was once a forest, permanently barren. A notable example of this is Easter Island.

Yes, because they can be replenished in a reasonable time frame

They are renewable because trees can be planted as they are cut down. The only problem with this is that it does take years for a tree to be fully grown.

Therefore, it can be argued either way.

Whether or not forests are renewable or not depends on how fast they are being destroyed in the opinion of many. If depletion exceeds a critical value, forests are permanently removed and hence non renewable.