To carry out horrific attacks on a global scale, the terrorists need methods of communication with people in other countries who share their radical views. Social media is the least expensive method of communication with large numbers of people across the globe. It is also one of the least secure ways to communicate. Law enforcement can monitor chats without the terrorists realizing they are being watched.
Yes, social media is a key part of the fight against terrorism. The enemy we are fighting is not an individual or a group, but rather a way of thinking. Recruitment for this ideology is done through social media, spreading the ideas and encouraging people to join. There are few ways to attack an ideology except to spread an opposite message through the same routes being used.
Terrorists themselves use social media to spread their messages of hate, as well as other broadcasted propaganda. There is nothing that a person can post on any social media platform that can stop a terrorist from being a terrorist. In this case, actions speak louder than words. Government and Federal agencies can monitor social media for terrorist activity, and perhaps foil a few plots. This will not, however, take down an entire organization. To eliminate terrorists, one would have to exert either power or peace.
With all the surveillance that's actually going on all around use everyday, it's unlikely that the average Twitter user is going to take down the next bin Laden. International, federal and local police agencies work in some very invisible ways investigating leads and other evidence of terrorist activity. However, staying alert in public and reporting suspicious activity using the immediacy of social media can alert authorities faster when there's a threat to public safety out in the open..