“Yinz” means you-ones or yous-ones (2nd person plural pronoun) and derives from the Scots language, sometimes called Lowland Scots, spoken in southern Scotland until the late 18th century. It was spoken by such famous people as Adam Smith and David Hume, who also spoke and preferred English.
Many Lowland Scots migrated to Ulster (Northern Ireland) around 1600, and many from there to North America, where they are known as Scots-Irish. Most originally settled in western Pennsylvania, including the Mellons (as in Carnegie Mellon University), who are from County Tyrone, Northern Ireland. This is why the Pittsburgh dialect is influenced by their language, and Pittsburghers are known as Yinzers today.