A pleiotropic gene exerts an effect on more than one trait. As
iain notes, sometimes a single gene will have multiple negative effects--a
single genetic mutation is responsible for all the symptoms of
Huntington's disease, for example. In other cases,
though, a gene will have both positive and negative effects.
For example, the apoe-2 allele decreases the risk of Alzheimer's
disease but increases the risk of heart disease; the apoe-4 allele has
the opposite effect. Along the same lines, people with sickle cell
anemia show greater resistance to malaria. Pleiotropy therefore raises
problems for genetic engineering and eugenics--you can't easily
produce a perfect organism, because optimizing one trait may
simultaneously weaken another.