A Recessive Gene is a gene that carries information in the DNA, i.e., hair, skin or eye color, blood types, straight or curly hair, etc. but is hidden (not visibly present).
A child inherits only half of their DNA information from each parent and in this combination generally display the dominant genes they received. If they inherited only recessive genes for some trait, that is the trait that is displayed. This is why siblings can look very different from one another and why a person with two brown-eyed parents can be born with blue eyes (brown eye gene is dominant, blue eye gene is recessive) if they inherited a recessive blue eye gene from each parent.