What is the Calvinist view of God's sovereignty?

I have many Calvinist friends, and when we discuss matters of theology or doctrine, almost inevitably, the conversation turns to them saying something like "That's because of God's sovereignty," or "That undermines God's sovereignty." In fact, most (if not all) of the 5 points of 5-point Calvinism hinge on the sovereignty of God as their cornerstone, either directly, or as they build on the other points. I have my own idea of what God's sovereignty means, but it must be quite different than what Calvinists mean by this phrase, because when they throw that phrase at me to support their views, I usually see my concept of God's sovereignty contradicting their view. So... what is the Calvinist view of God's sovereignty, and where is it based in scripture?