Ned's answer is partly right. Biologically there are two coloured genes which may be present to determine eye colour, blue and brown. Everyone has two of these. If a person has 2 blue genes they will have blue eyes, if they have 2 brown genes they will have brown eyes, and if they have one of each they will also have brown eyes as the brown gene is dominant over the blue one.
Each parent gives one gene each to their offspring, so two parents with blue eyes MUST have a blue eyed child, while two with brown eyes could have either. Let me know if there's anything else you don't understand.
By the way, any other colours eg green and grey are just versions of brown and blue respectively