Wizarding Social Classes
There are four types of "Wizarding Social Classes" that are displayed in the Harry Potter Series. These are Squib, Muggle Born, Half-Blood and Pure-Blood.
The name Squib is given to a child who is born into a magical family, but shows no sign of magic abilities. As the magic gene is the dominante one, most children are born a wizard or a witch, those that are not can still see the magic world, unlike muggles, so was given the name Squib. Notable Squibs include Argus Filch and Arabella Figg.
 Muggle Born
A muggle-born is a witch or wizard born to parents who are both muggles. Muggle-borns are frowned upon by many pure-bloods, who assume that they are not pure witches or wizards. Pure-bloods often give muggle-borns the nickname 'mud-blood', meaning dirty blood. Notable muggle-borns include Hermione Granger and Lily Potter.
The status half-blood is given to those who have only one magical parent.
Most wizards these days are half-blood anyway. If we hadn’t married Muggles we’d’ve died out. -Ronald Weasley.
Even with this said that most wizards are half-blood, they are still disliked by many pure-bloods, as they dirty the magical world with muggle blood. Harry Potter would be considered a half-blood, as his mother was a muggle-born witch, while his father was a pure-blood wizard.
Pure-blood wizards are wizards who are born into 'pure' magical families, whose members all have magical power. Some of these families believe that pure blood wizards should be the only type of wizards, like the Malfoys, but others think that half bloods are keeping the wizard race alive like the Weasleys. Families such as the Weasleys are considered "blood-traitors" by families such as the Malfoys.