Everyone knows the prophecies about Christ that are contained hin these chapters. "The virgin will be with child...", "For to us a child is born...", and A shoot will come up from the stump of Jesse...". Taken in that sense, they are obvious predictions about Christ. But what about context?
The chapters in which they are contained relate to the invasion of Israel, and the Lord's protection of the same. And this is where things get interesting. Double meanings. Yes, you heard (or rather read) me correctly. The propheices are God assuring his protection of Israel. Twice. Once against various enemies (Assyria, the Lower Kingdom, etc), and later against sin. These prophecies were fulfilled twice. The second time, they were fulfilled perfectly through Christ Jesus.