Pure-blood is the term for wizards and witches who have a purely or approximately pure magical heritage. This means that there are no Muggles in their family trees, but this is rarely, if ever, true if families are traced back all the way, for if wizards didn't mate with Muggles, their race would die out. Because the only way for a family to retain their pure-blood status is to marry other pure-bloods, all pure-blood families were related to one another by the 1990s. Because of inbreeding among pure-bloods and some marrying Muggles and Muggle-borns, the number of families claiming to be pure-blood is declining.
Pure-bloods are people who have no Muggles in their family. Traditionalist pure-bloods like to keep the generations "pure" by breeding with other pure-bloods and are generally the ones who use the term "Mudblood", a term considered derogatory by the wizarding world. Mudblood means Muggle-born, suggesting they have dirty blood and thus have no right to be a witch/wizard. Pure-bloods who do not share these prejudices are considered "blood traitors" by the ones that do.