Why your hair and eye colors change
Many babies are born with blue eyes, and then their eyes change color as their genes continue to develop. Hair color is the same way, sometimes, babies are born with very light colored hair that gradually darkens.
The colored part of the eye is the iris, it controls how much light is let into the eyeball and its color is determined by melanin, just like skin and hair. Darker colors absorb more light, and lighter colors reflect more.
Eye color is determined by a few different genetic factors, the most important being OCA2. OCA2 produced melanocytes, or melanin producing cells. Melanin is the protein that creates skin, eye and hair color. More melanin means darker eyes, hair or skin. The color of the melanin in the eyes is determined by three other genes, EYCL1, 2 and 3. Together, they account for brown, green and blue, but not hazel or grey eyes. Science is still working on how we get those.
All blue-eyed people can trace their ancestry back to a single human born between 6,000 and 10,000 years ago. Due to a genetic mutation, a human was born with a tiny switch right before the OCA2 gene, that limits the expression of the melanin -- kind of like diluting the stream of the protein. Individuals with albinism, or Albinos, have the OCA2 gene completely shut off. Their skin, eyes and hair have no melanin at all!
With this in mind, let's apply it to babies. When we're born, our genetics are decided, but the body hasn't necessarily acted on all the genes in your DNA. When it comes to eye color, the melanin controlled by the OCA2 gene is diluted and thus we all have blue eyes. For those with that blue-eye gene mutation they eyes stay blue. But for the vast majority of us, once we're born the OCA2 gene kicks into gear, creating melanocytes to make proteins and the eyes turn a different color, somewhere between 9 months and two years after birth. A medium amount of the melanin makes eyes green or hazel, a large amount makes them brown.
With regard to hair, the melanin builds up the same as in eyes, creating a dark color. As babies age, their melanin levels increase and their hair will darken. Hair colors can change well into puberty, as some genes aren't "switched on" until the hormones flood the body in adolescence. Eventually, usually in the 30s, human hair stops producing melanin and begins to turn grey. Basically, it stops adding color to the hair. Gray hair tends to occur earlier in Caucasians and later in Asians.
It's important to point out, that not all babies are born with blue eyes. This mainly occurs with Caucasian babies, maybe because of the lower levels of overall melanin due to the lighter skin tone. Babies of Asian, African and Hispanic genetic heritages will likely be born with dark eyes that stay dark.
Funnily enough, 10-15 percent of Caucasians report their eye color continued to change into adulthood, so it's possible your peepers are still not settled!