have a look here: http://www.horiba.com/scientific/products/particle-characterization/education/sz-100/particle-size-by-dynamic-light-scattering-resources/what-is-z-average/
Number mean is the size of the particles based on their number average. If you know the principles of light scattering you know that you have a laser beam going through your sample. If your sample has particles, they scatter the incidental light which is detected at an angle (usually 90 or 173). Big particles, more light detected. Clear?
Now, if I have 1000 small particles and 1 big particle, the intensity of the light detected is going to be closer to that of the small particles (in the absence of the big particle). If I have 10 small particle and 10 big ones, the intensity is going to be much closer to that of the big particles. However, there is an expression that can determine how much of the scattered intensity belongs to something big and how much to something small. Actually there are three of them. One does it in terms of intensity, the other one in terms of volume and the last one in terms of number of particles. There's more into it but for now that should tell you all you need.
PDI is the polydispersity. If I have 50 particles of 10 nm the PDI = 0 (for a zetasizer). This means that all my particles have the exact same size. If I have 50 particles of 10 nm and 50 of 100 nm, the PDI will increase. Usually, a nice sample is less than 0.1 (for a zetasizer).