Genetics aside, what are the biochemical reasons the different colours of human irises?
Also, related, how does eye colour change, particularly in childhood? (example: my eyes used to be blue, but are now greenish-hazel).
The colour of human eyes is determined by the pigmentation present and the scattering of light. Variance in the colour and density of the pigments affects how light is absorbed and reflected causing the different iris colours we see. Wiki has a fairly comprehensive coverage on the topic so,I'll use a few of the wikipedia examples to explain how the pigmentation and scattering of light interact to give colours:
Blue eye colour is the result of pigment in low concentration and Rayleigh scattering (or Tyndall effect) of the short light wavelengths (blue is short, red is long).
Brown eyes are the result of higher melanin concentrations which absorbs more of the light, reducing the amount of light being reflected.
Green eyes appear to be mid-ground between blue and brown, they have more pigment than blue but less than brown.
What is Rayleigh scattering / the Tyndall effect and why do they turn eyes blue?
I shall refer to this as the Tyndall effect but in the literature both Rayleigh and Tyndall are used because they are apparently very similar though Tyndall occurs with much larger particles. The Tyndall effect is caused by the variable scattering of light by particles depending on the wavelength of the light and relative size of the particles. Shorter wavelength lights are scattered more than the longer ones (so more red light is absorb than blue) which means more blue light is reflected. When more melanin is present in the iris it will better absorb the short wavelength light than when there is little melanin, therefore, people with low melanin levels appear to have blue eyes.
Why do eye colours change?
Again, wikipedia has a fairly thorough section on this and I will just summarise and directly quote it. Eye colour can change because the melanocytes responsible for the pigments have to continually produce pigment and, just like those causing colour in hair, they can become less productive (which is why we have grey hair) and this happens more with age. Infants often have blue eyes that turn dark, just like yours did, because the melanin is gradually accumulated - it just takes time for enough pigment to build up and allow the eye colour to match it's genetic determinants:
In this study 10-15% of those studied had changes in eye colour beyond childhood so, al though colour is generally stable past childhood, it is not uncommon for eyes to change, and this is likely due to changes in melanin composition. This study is an example of clour change in birds too.
A side note: Animals with other colours
It is common for animals to have other eye colours, for example Blackbirds (Turdus merula) have an Orange eye, which is caused by Carotenoid pigments, rather than melanin as in humans. The reason they have this could be as an indicator of quality in courtship - carotenoids are hard to get, males with bright orange eyes therefore have access to good food resources, and female blackbirds find that attractive. (This section is all from my memory after a talk with a tutor on my undergrad field course in the Isles of Scilly).