Law (which corresponds to the commands of Scripture) is what God demands of his image bearers, and gospel (which corresponds to the gospel declarations of Scripture as it relates to the person and work of Christ) is what God gives freely out of sheer grace.In other words, anywhere in the Bible where there is a command we may call law. Anywhere in the Bible where there is an unconditional promise we may call gospel.
Understanding how these two words are different yet interact is incredibly important. Michael Horton quotes Theodore Beza (1519-1605, John Calvin's successor): "The confusion of law and gospel is the principal source of all the abuses that corrupt or have ever corrupted the church." Another Modern Reformation article quotes Luther: "Luther even declared of the person ignorant of this [law/gospel] distinction that 'you cannot be altogether sure whether he is a Christian or a Jew or a pagan, for it depends on this distinction.'"
For me, and many others I would guess, having been immersed in a Dispensational church culture, the tendency is to view "law" as the stuff of the Old Testament and "gospel" as the New Testament. In other words, law was then and is no longer. This is what's so radically different about the Reformation perspective: both law and gospel are at play throughout all the Bible. Therefore even our lives today need to be shaped by both law and gospel.
Seeing all the Bible unified around a law/gospel theme is correlated to seeing all the Bible unified around Christ. In Sally Lloyd-Jones's children's book, the Jesus Storybook Bible, she shows how Old Testament stories are really types and shadows of Jesus (gospel), not stories of moral heroes that we ought to try to be like (law). If a kid's Sunday School lesson is "dare to be a Daniel," that is, God wants you to try real hard to be brave like Daniel was, then not only did we miss the point of Daniel but we've given those kids all law and no gospel. And that means no Jesus. The fruit of this is kids who are either Pharisees or Philistines, moralists or rebels.
A man spoke the truth, but people rejected him. They executed him. He descended into the pit of death. But he miraculously emerged alive! Is this the story of Daniel or of Jesus? Daniel is a type of Jesus, a foreshadowing. Daniel was saved from death by trusting in God. The Sunday School lesson from Daniel should be to trust in Jesus for salvation.
Today this fresh perspective of the Old Testament may be perceived as a new fad in how we approach the Bible, but the reality is that this view goes back to at least the time of the Reformation. And, of course, if you hold this view you may also argue that the apostles and even Jesus himself (Luke 24:27; John 5:39,46) had this perspective of the Old Testament.
Jesus Christ himself stands as the solution to the law/gospel antithesis. That's why understanding law/gospel is so important: to confuse them together or to utterly separate them, to err on either side, is to lose Christ.