Everyone has 2 genes making up eye colour, each of these may be either blue or brown. Each parent gives one of these to their child, so the child will have two as well. The brown gene is dominant over the blue one, so if they have one of each, they will have brown eyes.
In answer to your question, the parent with blue eyes will pass on a blue gene (as they don't have any brown ones), and the parent with the brown eyes must have one brown, but the other one could be either. Therefore it depends what the second parent gives to the child as to what colour the child's eyes are.
Hope this makes it a bit clearer - A Level Biology!!!