Cardboard, when not made of recycled materials, is typically made of Kraft paper, which is the same brown paper that many paper bags are made of. Kraft paper is made of wood that has been pulped. It is pulped mechanically (ground and crushed), then chemically using sulfates or sulfites.
Once the cardboard has been put in the recycling, brought to a sorting facility, and baled, it goes to a processing plant. At those plants, the cardboard is soaked to break it down, mixed with new wood fibers to strengthen it, and made into more cardboard. Cardboard can go through this process 5-7 times before it is no longer able to be recycled because the fibers it is made of break down enough that they cannot be remade into cardboard or other things. In 2018, about 96.5 percent of corrugated cardboard in the US was recycled. It is unclear whether this means 96.5 percent of cardboard made its way to recycling facilities or if it was remade into other things. Either way, that’s really impressive.
https://www.themanufacturer.com/articles/how-a-cardboard-box-is-made/
https://stlcityrecycles.com/how-many-times-can-this-be-recycled/