There are many genes involved in eye color. It's the combination of genes that affect our eye color, and since we're not genetically identical to our parents we're going to have a different combination to them (and therefore a significant possibility of different eye color). Our genes are in pairs (and in each pair the two genes are different versions, called alleles). One of the pair comes from our mother, the other from our father.
There is a myth that eye color is determined by one gene; the myth goes that there's a dominant brown eye gene, and a recessive blue eye gene (meaning that if you have a brown eye allele and a blue eye allele, you'll have brown eyes). By this idea, to have blue eyes you need two blue eye alleles. Since you only have blue eye alleles, then you and your blue eyed partner can only pass on blue eye alleles and so any offspring must have two blue eye alleles and therefore blue eyes.
However, as I said, this one-gene model for eye color is a myth. More precisely, it's a convenient simplification used in schools which is never corrected. There are many genes affecting eye color, not just one. People with blue eyes will have a variety of genes and the combined result of this gives them blue eyes. Since their child is going to have a different combination of genes they could have a different eye color.
To summarize that, there's nothing at all unusual about brown eyed people having a blue eyed child. There is nothing here in the slightest to suggest that you're adopted.
lol i wanna know now too
The milk man did it...
You can't go by that. One of your parents could've been a carrier for a trait (they didn't have it, but they passed it on to you). Ask them, and get tests if you're worried. Not all of your family had blue eyes :)
Well in simple mendelian inheritance it would show as theoretically impossible for their offspring to have brown eyes due to both the parents having "bb" genes. Thats saying okay if i cross bb with bb i can get any B. Just think of trying to multiply 1*1 and get 2 its not going to happen, but real genetics for eye color are not as simple as crossing two alleles and saying that something is impossible without going into too much detail, eye colors have multiple factors of genes, therefore it is very unlikely, but possible that with two blue eyed parents (bb) could have a child (Bb) (BB) depending on natural variation, and other genes that make up eye color.