Firstly, the wet surface lessens scattering, forcing more light into the cloth.
Secondly, the water fills up the holes between the cloth fibers and causes even less reflection and scattering between the particles. It leads the light even deeper, causing more absorption and makes it easier for the light to reach the other side.
Finally, some of the light that is reflected out of the material by the cloth, is then reflected back into the cloth by the layer of water.