Why Prussian blue 'blue' in colour?
Prussian blue contains both $\ce{Fe(II)}$ and $\ce{Fe(III)}$. Mixed-valence compounds, such as the one in question, absorb certain wavelengths of visible light resulting due to the phenomenon of inter valence charge transfer (IVCT). 
General Scheme for IVCT is:
$$\ce{L_nM^+-bridge-M'L_n + h\nu -&gt;L_nM-bridge-M'+L_n}$$

In this case, orange-red light around $680\ \mathrm{nm}$ in wavelength is absorbed, and the reflected light appears blue as a result.

Additionally, changes colour from blue to colourless upon reduction. This change is caused due reduction of the $\ce{Fe(III)}$ to $\ce{Fe(II)}$, and thereby eliminating the IVCT responsible for Prussian blue's namesake blue colour. This is also why Prussian Blue exhibitis electrochromic behaviour.

For a more detailed description read this and this. Alternatively, you can look it up in a textbook.