You inherit one set of genes from your mum and another set from your dad.
Imagine the gene for brown eyes is B and the gene for blue eyes is b. The blue eye gene is recessive and the brown eye gene is dominant. Someone with just one B gene has brown eyes, you only have blue eyes if both sets of genes are b.
Your mum must have Bb genes - one B and one b. She therefore has brown eyes, because the B gene is dominant over the b gene. Your dad has blue eyes, so he must have two copies of the b gene.
When eggs and sperm are made only one set of genes is included, so when fertilisation takes place the baby gets only two sets of genes, one from the father and the other from the mother.
Your dad can only give you a b gene, because that's all he has. Your mum has a choice, she can give you a B or a b. If her egg contains a B gene, the child has brown eyes like your siblings. If her egg contains a b gene, the child has blue eyes like you. It's a 50/50 chance, so to have lots of brown eyed siblings is a little unusual, but not impossibly so.
My explanation is all a bit simplistic, most traits have more than one gene so it's a bit of a complex picture. Hope it helps :)