Here's a weird fun fact: almost nothing in nature is blue.
You may say, "but the sky is blue, you idiot." While that is something we're taught since we were small, the truth is that the sky just appears blue. This is due to the Tyndall effect, or the way light reflects off of scattered particles.
Even birds you might think are blue, like the blue and yellow macaw, only appear blue because of nanochannels within their feathers that alter the way light reflects. So if you've got blue eyes, you guessed it, there's no blue pigment in there. But why do they look the way they do?
In the iris, there are two layers of cells: the stroma and the epithelium. In dark eyes the stroma contains melanin, but in blue eyes it is translucent.
Due to the genetic mutation that makes it completely clear, the stroma scatters the light waves.
The color blue travels in shorter waves, so it scatters more easily and is more visible. Eyes are blue because it's the easiest color to reflect.
This is also why blue eyes can appear different in different lighting or settings. The light is just reflecting differently on the stroma.
In gray eyes, the effect is similar, but replacing the melanin is collagen, which dampens the blue reflection.
(via IFL Science)