Basically every physical trait you have is controlled by 2 genes, some of which are more dominant than others. Every egg and sperm contains half of these genes (so 1 gene for each trait) and when the egg is fertilized the dominant gene controls the features.
Brown is a dominant eye colour gene, whereas blue is recessive, therefore each parent will have at least one brown eyed gene. To have blue-eyed children the sperm and egg must both have contained the blue eyed gene, meaning that both you and their father have one brown eyed and one blue eyed gene.