explain why with specific details and examples
I'm going to disagree somewhat with the answer provided earlier. Gitlow is a case from the U.S. Supreme Court that established that the right to Free Speech is not absolute. In other words, there are some situations where certain words and statements may be punished by the government -- including by arrest and conviction. The case impacts today's society very much. It is still good law, and it is the basis under which people are arrested for certain types of speech.
This opinion is available online, and I encourage the questioner to read it. Opinions are written by a judge or justice, on behalf of the court or a group of judges/justices, to explain the reasoning behind why they ruled the way they did. The Gitlow case is "precedential" -- this means it is still good law today. The principles expressed by the Court in this opinion are still applicable and still enforced today.
If you're writing about why the case is important, here are the questions your essay should answer:
1) Under what precise situations might someone be arrested for something they say?
2) Is there a difference between arresting someone for words and arresting someone for actions? Should there be?
3) The opinion contains a "dissent" -- a sort of second opinion by a Justice (in this case it was Justice Homes) that disagrees with what the majority of the Justices decided. Which opinion do you agree with most and why?
4) What are modern examples of speech for which someone might be arrested? Where could this speech occur? Facebook? Twitter? Could someone be arrested for their speech in these more modern forums?
Finally, as was mentioned in the earlier answer to this question, this case does rely on the 14th Amendment to apply Federal Constitutional Principles to the states. But this case is not the case that decided that issue, this case merely relies on that as a matter of law. So while that point is true, it is not necessarily a vital issue to analyze when asked to look at the unique features of this particular case.