The clear and present danger was carved out of the First Amendment by the U.S. Supreme Court's 1919 decision in Schenck v. United States. You can find a great written summary of that case by PBS here and by the American Bar Association here.
In that case, Schenck, was involved in encouraging resistance to the World War I draft, and was charged with violating the Espionage Act by obstructing military recruitment. The only question for the Court to decide was whether Schenck's words and actions were protected by the First Amendment. The Court ruled against Schenck, but in its most memorable phrase, declared that
The most stringent protection of free speech would not protect a man in falsely shouting fire in a theatre and causing a panic. ... The question in every case is whether the words used are used in such circumstances and are of such a nature as to create a clear and present danger that they will bring about the substantive evils that Congress has a right to prevent.
The Court clearly was influenced by the historical context of Schenck's actions.
When a nation is at war, many things that might be said in time of peace are such a hindrance to its effort that their utterance will not be endured so long as men fight, and that no Court could regard them as protected by any constitutional right.
The Times story summarizes the law on clear and present danger, and then updates it today. Apparently, some legal scholars say that current online recruiting efforts by the Islamic State justify a reexamination of that now 96-year-old precedent. Those scholars say that law enforcement and defense officials need greater authority to suppress speech that encourages violence but does not yet advocate a clear and present threat of such violence.
Sharing this story with your students could be part of an engaging activity. First, poll them on this question: Are First Amendment freedoms absolute, or are there situations where Free Speech can be limited? Then, guide them through a discussion where it might be possible to limit free speech (examples might include obscenity and defamation). (This thorough, 35-page report by the Library of Congress's Congressional Research Service offers an exhaustive discussion of First Amendment exceptions). Next, ask them whether they have ever heard the expression, "You can't shout fire in a crowded theatre." Ask what that expression means. Then show them this news story and ask them to write case summaries of Schenck and later cases on this topic. Lead the class in a discussion of whether current Islamic State threats justify modifying the Schenck rule. Conduct a re-vote on the initial question near the end of the lesson, then ask students to write a paragraph summarizing how their thinking about the First Amendment was affected by today's lesson.