You've seen the recycling logo, three arrows pointing around in an endless loop.
This is a little misleading though, because you just can't recycle the same piece of paper endlessly.
A sheet of paper is made of interlocking fibers, which originally started out as wood fibers suspended in water, a mixture known as pulp. As the pulp dries, the fibers stick together in an interlocking pattern.
A good way to picture this is to imagine a bunch of cooked spaghetti. Instead of eating it, pour it out as a flat layer on a cookie sheet, then bake until it's dry. The result, a big, flat mass of dried spaghetti, is like a fresh sheet of paper. They both hold together because of their dried-out interlocking fibers.
When you recycle paper, the paper is mixed with water, then ground up in a machine like a giant blender. This turns the paper back into pulp, but this new pulp isn't exactly the same as what we started with. All the blending and grinding has shortened and weakened the fibers. When you make recycled paper, it's weaker and easier to tear, because the interlocking fibers aren't as long or strong. Imagine breaking up our spaghetti mass and recooking itthe noodles will be a lot shorter this time, and won't lock together as well.
How many times could you recycle a single sheet of paper before the fibers got too short and weak to hold together? Perhaps six, but it never really happens that way. Recycled paper pulp is usually mixed with some virgin wood fibers, to hold it all together.