A carrier for red-green colorblindness
A "carrier" of a gene is someone who has a copy of a gene for a recessive condition, but does not show the trait. Color blindness is a sex-linked trait. This means it is determined by information on the 23rd set of chromosomes--the XX or XY chromosomes that determine the sex of an individual. The gene for color blindness is carried on the X chromosome. If the gene is present on the X chromosome of a male, there is no "good" gene for color vision to block it; that would have to be on another X chromosome, and he has a Y. The male is then color blind as a result of receiving the gene for color blindness on the X chromosome he got from his mother--who is the carrier.
Because women have two X chromosomes, they are far less likely to actually be color blind themselves. They are therefore carriers of the trait if they have a gene for color blindness on one of their X chromosomes. There are women who are color blind but they are far more rare. These women have received the gene for color blindness on the X chromosome from their mother, and also on the X chromosome from their father. This means that a color blind woman must have a color blind father, as he only has one X chromosome--which has the gene for color blindness.