Brown spots on the eye ball are merely just pigmentation. It can be caused by your ethnic race, for example many asian people have ocular pigmentation. It is basically caused by the melanin that defines skin colour. You can have pigmentation in your eye if you have dark hair colour, or darker skin colour. If you do have pigmentation in the eye, it is advisable you see a doctor, and possibly have a biopsy done.
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Blue eyes with brown flecks or blue eyes with a brown dot are caused by a person's genes. In researching this answer, I couldn't find a good explanation as to why blue eyes with brown spots occur. Scientists have discovered that blue eyes did not exist a few thousand years ago. The ancestors of people with blue eyes had brown eyes; a genetic mutation caused blue eyes. You could hypothesize that since the ancestors of blue eyed people had brown eyes, the brown dots sometimes found in blue eyes are simply another result of the genetic mutation.
This a normal variation in the iris. Some security systems are based on the patterns of color seem in everyone's iris.