Muggles. Wizard's word for non magical people. Read about the community between the 'Moodles' and the people with magical powers. I.E. Wizards.

In the world of Harry Potter, there is an almost total divide between those people who can use magic, and are permitted to know of its existence, and the much more common Muggles who have no idea that magic is real. A select few Muggles are in on the secret, including high ranking government ministers (the Prime Minister certainly and possibly others) and those muggles who have a witch or wizard in the family, like the Dursley family and Hermione's parents.

The reason for the total secrecy (and consequentially the modification without consent of Muggle memories) is manifold, including Muggle mistrust and even fear of magic users and the fact that the magical community refuses to provide magical assistance to Muggles. The persecution of the middle ages gave rise to the concealment of magic, and the wizards and witches of the world could never hope to provide magical solutions to all of the Muggle's problems.

However, it is interesting to speculate on how much assistance Muggles do receive, through official channels. The world's governments are aware of magic and it seems very unlikely that they would be content to allow magic users to rule themselves.