Privacy is becoming an increasingly important aspect in distributed systems. In anonymous communication, privacy is provided to communicating parties by hiding their identities from each other and/or from others. This paper discusses the problem of anonymous communication and clarifies the notion of anonymity. We use Tor as a case study to illustrate the security goals of anonymous communication, and outline the threats to which Tor is known to be exposed. To demonstrate anonymity quantification, we apply an information theoretic metric to the example Tor scenario.