Twitter is built around short messages or "micro-blogging." Hashtags can help users follow class conversations there.
Social media is a huge category with vague edges. A leading example is Twitter, a place where users can post things for others ("followers") to see. At Twitter, instructors and students can microblog or "Tweet" short updates, links to content, and pictures in a feed that other class members can follow by using hashtags.
Some faculty have used social media sites like Twitter, Instagram, and even Facebook in classes successfully, and it's tempting because it's so widespread. But there are two considerations to doing so:
Do you use social media to communicate with friends, family, colleagues, or perhaps a broader following? If not, then using it to communicate with students may be more trouble than it's worth. After all, it's one more thing you must learn.
Your students probably have social media accounts, but they may not. Students who do use it might be reluctant to mix their academic and private life by using an existing social media account. If work in social media is a major part of your course, you could ask them to create an account just for your course. But be sensitive to student reluctance or objections.
If you have specific, describable reasons for using social media in your class that are related to learning goals or objectives, then proceed. If not, and you really just need a place for asynchronous discussion, consider D2L instead.