Let's talk about phishing. Phishing is just like fishing, only your identity is the fish and the bait is an email that looks like it came from your bank, or eBay, or Paypal, or any other legitimate place. The goal is to get you to follow a link to a site owned by the phisher, and trick you into divulging some private information, such as your bank account number, pin, passwords, or social security number.
Some phishing emails look completely legitimate, using logos, links, and text from the real business. Many try to warn you about fraud being committed with your account--the truth is, the senders of the email are the ones trying to commit fraud with your account, if they can trick you into divulging it. These types of emails are almost always fake. When you follow the link in such an email, you'll usually get taken to a web site that looks exactly like the real web site. But it's not.