In a microscopic view, the paper tower is made of many tiny fibers. Those fibers act like capillary tube. Capillary tubes have many characteristics. One of them is called capillary effect which means that water (or liquid) will clime higher inside of the capillary tube than the surface of the water outside of it.
From a macroscopic view, however, we cannot see those tiny fibers. What we see is a collective result of thousands of thousands of fibers working together and it shows that water is soaked up by a paper tower.