Why is water transparent?
Water is not, in fact, colourless, but is slightly blue. As you can see below, in the visible range, there is slightly more absorption toward the long wavelengths, so more blue light makes it through than redder light. However, the absorption is very low in the visible range so the blue colour is faint and not apparent unless looking through a significant thickness of water. The reason things like $\ce{Cu^2+}$ solutions appear so vividly blue is because they also absorb red light, but very strongly, so a good deal more blue light than red passes through the solution. (see here)

I'm not sure exactly what you mean by transparent here, but if you mean why isn't water opaque, because water doesn't absorb much visible light (as described above), and doesn't contain any non-uniformities (like particles or the fat globules in milk) that can cause scattering, photons can travel through water in a straight line and most make it through without being absorbed, making water colourless (when looking through a small quantity) and transparent, much as air is.



Source