Academia.edu is like the LinkedIn for academics. It is a great way to connect with your academic peers and search for articles. Like LinkedIn you are able to create a positive profile aimed at a particular audience. In essence the perfect target marketing tactic.
It is a way of sharing your own articles for other academics to view openly. The one feature of Academia.edu is its in-built analytical tool so you are able to manage your own profile page and the articles you upload.
If you are studying or working in academia, it is as much an important tool to you as LinkedIn is to other professions or job seekers.
When you log in to Academia.edu, you can do so through your Google+ account which automatically links the two together so I would suggest creating a Google+ account with the same profiles again, same links as the information are quite similar in both.
Google+ allows you to connect with communities similar to those like the groups in LinkedIn. I hope you can the pattern emerging here between all the social media platforms. The way you use them depends on your desired target audiences. One may use a particular social media platform over another. Keep in mind you are targeting human beings here.