The Constitution is still relevant today in two main ways.
First of all, the Constitution does still lay out the basic set of rules that governs how our country is run. When the Supreme Court says that a particular law is unconstitutional, that law is no longer in force. This can have very serious consequences. For example, the most recent election cycle was impacted strongly by the Supreme Court’s interpretation of the First Amendment. The Court’s decision in Citizens United allowed “Super PACs” to spend unlimited amounts of money promoting or opposing certain candidates. In particular, this affected the Republican primaries in a major way.
Second, the Constitution is still relevant because it is a major source of legitimacy for people’s ideas. Because we revere the Constitution, people are continually referring to it as a way to argue that their ideas are more compatible with basic American beliefs than those of their opponents. For example, the Tea Party talks constantly about how certain things the government does go beyond the Constitution. They use this claim to bolster their arguments for smaller government. Gay rights advocates, by contrast, point to the Constitution as a foundation for their claim that they should be allowed to marry.
In these ways, the Constitution remains relevant both as a source of actual law and a foundation for political arguments.