Blue eyes get their color the same way water and the sky get their blue color. They scatter light so that more blue light reflects back out.
People with blue eyes have no pigment at all in the stroma, causing the fibers to scatter and absorb some of the longer wavelengths of light that come in. More blue light gets back out and the eyes appear to be blue.
SciShow just did a thing explaining odd conversations that can effect the whites of your eyes, as well as other things like skin. Strangely, they didn't talk about that colloidal silver guy who turned Smurf-ass blue.