Phishing scams are typically fraudulent email messages appearing to come from legitimate enterprises (for example, your university, your internet service provider, your bank). These messages usually direct you to a spoofed website or otherwise get you to divulge private information (for example, passphrase, credit card, or other account updates). The perpetrators then use this private information to commit identity theft.
One type of phishing attempt is an email message stating that you are receiving it due to fraudulent activity on your account, and asking you to "click here" to verify your information. See an example below.
Phishing scams are crude social engineering tools designed to induce panic in the reader. These scams attempt to trick recipients into responding or clicking immediately, by claiming they will lose something (for example, email, bank account). Such a claim is always indicative of a phishing scam, as responsible companies and organizations will never take these types of actions via email.