Pleiotropy is the multiple effects of a single gene. In other words, it is when a single gene controls several phenotypic traits. These traits may be seemingly unrelated.
A classic example is the human disease PKU (phenylketonuria). A mutation in a single gene that codes for an enzyme needed for the metabolism of the amino acid phenylalanine causes mental retardation, and reduced hair and skin pigmentation.
The term pleiotropy comes from the Greek pleio, meaning "many", and tropo, meaning "changes".