A recessive gene is a gene that can be masked by a dominant gene. In order to have a trait that is expressed by a recessive gene, such as blue eyes, you must get the gene for blue eyes from both of your parents.
You might remember the word recessive from biology, where it most often appears. Its opposite is dominant and is always living in its shadow. A recessive allele has to team up with another recessive allele in order to show up. We can also use recessive to describe something that has the tendency to withdraw or recede, or something pertaining to an economic recession.