Water molecules have several qualities which make them unique. First, water molecules are dipolar which means one end of the molecular structure of H2O is more positive and the other is more negative. This molecular structure allows for surface tension, adhesion, and cohesion. If you can remember back to your middle school science class, these are the properties that allowed your daisies or celery sticks to turn the color of the dyed water you'd set it in a few days prior. Or more basically, these properties explain how paper towel works, you can simply watch the water "climb" the paper towel if you just set one edge in the moisture.
The same way that water climbs its way through plants, or up your paper towel, it can climb through the pores of the materials of walls, which is capillary moisture. Cement, wood, cinder block, plaster, brick, (and more) are all materials which have pores and are susceptible to rising damp.
Note: If you are unsure if your problem could be rising damp, please feel free to take some photos of the affected area and include some basic information when you contact our company.