Facebook is a social utility that connects people with friends and others who work, study and live around them.
Facebook is a platform for integrating a variety of tools rather than a single tool – by logging into Facebook one can use chat tools, discussion boards, image galleries etc. Within an academic context perhaps the most popular use of Facebook is using the 'events' facility to alert people to for instance lectures, debates and discussions.
It should be noted that the design of Facebook is influenced by its primary revenue-generating channel which is through context-sensitive advertising. Today its primary use seems to be non-academic where friends can alert each other to pictures they've taken, music they like, films they've watched. Students do sometimes use the communication tools to discuss academic work and life.
Ways of using Facebook
What makes Facebook special is that it can be used to connect to a very large number of people. So perhaps the primary academic use of Facebook is in alerting people to events that are happening, new papers, experiments that need volunteers, new projects etc.
As with most internet applications people should take care that they only share the information about themselves that they are happy for others to know. Of course this relates to passwords, email addresses, and postal addresses but it may also include affiliations and niche interests. Identity sharing is a matter of personal choice, but one you need to have an opinion on.