Wax paper is paper coated in wax, and wax belongs to a large class of organic chemicals that are hydrophobic. Organic chemicals contain carbon, and tend to not be mixable with water (with certain notable exceptions like alcohols). When it's 2 liquids that encounter each other, it just means that if you don't stir them constantly, they will separate out into 2 layers. When it is water and a solid, such as the wax coating on wax paper, it results in hydrophobicity.
Hydrophobic means, literally "afraid of water." In terms of chemistry, it refers to the degree to which water forms into beads or spreads and flows across the material. Without getting into the specifics of defining it, something that forms large beads of water on the surface, (glass, wax, ceramics like that in your bathtub, etc) are hydrophobic, while those that get wet easily (unvarnished wood, concrete, etc) are very much not hydrophobic (they are hydrophillic, or water loving). Water slides off of wax paper because it is hydrophobic.
Looking through my course notes on hydrophobicity, it's somewhat difficult to explain exactly what causes this property, but it involves surface tension. There is a surface tension between any phase interface - where solid touches liquid, solid touches gas, or liquid touches gas. These properties define the work of adhesion as surface tension of solid to gas + surface tension of liquid to gas - surface tension of solid to liquid (the Dupré equation), and the work of cohesion as double the surface tension of liquid to gas. When these values are known, the interface angle between the solid and liquid is determined to be the arccosine of 2 times Work of Adhesion divided by Work of Cohesion, minus 1, or arccos((2A/C)-1) This gives you an angle in degrees, from 0 to 180. 180 degrees refers to perfect hydrophobicity - the drop of liquid will form a perfect sphere and roll along the solid - and 0 degrees refers to perfect hydrophillicity - the drop of liquid will spread into a flat layer along the entire surface of the object (assuming nothing else stops it, like gravity, and assuming you wait long enough). For wax paper to have water sliding on it, this requires A/C, work of adhesion divided by work of cohesion, to be a small number. Going back to the definitions of these work values, this means the surface tension of solid to gas for wax is very low, and/or the surface tension of solid to liquid for wax is very high, since for water to slide on a surface, the angle has to be high, which means cos(angle) must be close to -1, which corresponds to an A/C value close to 0. In short, it goes to surface tension properties between the wax, the water, and the air.
I hope it helps
