Phishing is an attack that tricks the user into visiting a site that they believe to be something else.
It normally takes the form of an email from a bank, suggesting that your account will be closed unless you update your details by clicking the link in the email to log in.
This then takes you to a fake bank or PayPal page that looks exactly like the real thing, and then the 'Bad Guys' collect your username, password and login details so that they can drain your bank account of all of its contents.
Never ever ever click a link in an email, especially one claiming to be a financial institution.
Hopefully common sense will prevail, as these emails are often full of grammatical and spelling errors, and rarely name the recipient by name.
A legitimate bank email (and there are very few) will know your name.
The safest tip in this situation, is to manually enter your banks web address into the bowser i.e don't use a link to get to it, and log in via your normal means. This way, you have a bteter idea that you are going to where you thought you were going.
Also consider using OpenDNS. By manually routing your internet traffic through the OpenDNS servers, you will prevent a number of malicious and phishing websites. Read all about it on their website for more details.