What does "phishing" mean?

"Phishing" is a technique used by abusers of the Internet to trick legitimate users into revealing their credentials; i.e., their usernames and passwords. This is typically done by sending e-mail to the user -- you -- purporting to be an urgent message from the system administrator requiring that you "upgrade" or "validate" your account by connecting to a URL that will ask you for your username and password.

Once you've been "phished", the abusers will use your credentials to log into your account remotely, and will probably send vast quantities of spam from it in your name. To stop the spam, the real system administrators will have to block all access to your account. For lots of detail, see the Wikipedia article on phishing.

How can I tell the difference between "phishing" and genuine e-mail from the real system administrators?

This is easy. Real system administrators will NEVER ask for your password. They don't have to, The have all the necessary privilege to administer the system without your password. They may occasionally ask you to change your password, but they will never need to know it.

A nice primer on phishing is available from the Anti-Phishing Working Group.