Actually, that is a good question, since it used in different ways, but all relating to the same basic thing:
Sex-linked gene: a gene (or piece of genetic information) that is contained on a part of the sex-chromosome that determines the sex of the offspring. Males have 2 long matching chromosomes, and females have one long, and one short. Offspring inherrit one from each parent. Each get a long chromosome from the father, and either a short or a long from the mother: if they inherrit a long one from mom, the baby will be a boy (2 long chromosomes), and if they get a short one it will be a girl (one long from dad, and one short from mom). Any genes contained on the part of the long chromosome (in both males and females) that is missing on the female shorter chromosome is a sex-linked gene. Female offspring would only be able to inherrit these genes from the father, since the mother didn't donate any due to the chromosome being shorter.
How does that relate to color breeding?
Well, Brown dilution for example: let's take a chocolate male and a black female. Brown dilution is carried on the sex-chromosome. So dad (the chocolate male) would carry 2 recessive brown dilution genes. The female wouldn't carry any, because she only has one loci for this gene because she is "missing" the second long-part of the chromosome, so she would only need one recessive brown dilution gene for it to show (it would have no competition for dominance). And she is black, so she has no brown dilution. So you mate these 2 ducks, and all babies inherrit one brown dilution gene from dad, but none from mom. All males babies will have one brown dilution gene, but also one dominant non-brown gene. All males would be phenotypically black. The females however, would all inherrit one brown dilution gene, but no other gene to compete with it. So all females would be brown.
With chickens the barred pattern is sex linked. That's why you can cross a red rooster with a barred hen. All male offspring will be barred, and females are black/brown.
This comes in handy when you want to know the sex of the babies so you can choose and raise them accordingly.
