Muggles' Guide to Harry Potter/Magic/Muggle-born

Overview
A Muggle-born is a witch or wizard of non-magical (Muggle) parentage. Muggle-born witches and wizards are looked down upon by some Pure-Blood wizards, who think that purebloods are superior and Muggle-borns are unworthy of magic.

Extended Description
Famous examples of Muggle-born witches are Lily Evans and Hermione Granger. We are told that Justin Finch-Fletchley is Muggle-born as well.

In Harry Potter and the Chamber of Secrets we are introduced to another name for those witches and wizards born of Muggle parentage - "Mudbloods". This is an insult used only by purebloods who feel that Half-blood and Muggle-born witches and wizards are somehow inferior to purebloods.

Analysis
Apparently it is not necessary to have magical ancestry to be able to do magic oneself; it seems that magical ability can spontaneously appear without known magical ancestry, and sometimes in only one child of a given union. Lily Evans' sister Petunia showed no sign of magical talent, though her son Dudley may have shown a hint of ability.

Through a process possibly akin to hybrid vigor, it seems that many of the most powerful wizards have some Muggle in their recent background. Interestingly, it seems that powerful wizards and witches can spring directly from Muggle roots as well: Lily Evans and Hermione Granger are noted to be highly gifted Muggle-born witches.