Recycled paper consists of wood fibers, just as regular paper does. When paper is soaked in water long enough, the fibers separate and (after washing to get rid of ink and so forth) they can be re-pressed into paper.

The only difference is that wood fibers are degraded by the recycling process, so all recycled paper has to contain some virgin wood pulp to maintain acceptable strength and quality.

See

• This previous answer
• This website on paper recycling