Muggles are non-magical people. They often have very irrational views towards magic, which caused witch hunts in the 10th century. In the 20th century, Muggles are less likely to burn someone alive, but still are wary of magic when it appears. Memory charms are used frequently in order to keep muggles from learning about magic.
It is not unusual for two muggle parents to give birth to a witch or wizard, or to unknowingly marry a witch or wizard. When this happens, they can either be carefully kept in the dark, or can live with the knowledge of the relation.