Typical severity: Very High. Likelihood of attack: High. Phishing is a social engineering technique where an attacker masquerades as a legitimate entity with which the victim might do business in order to prompt the user to reveal some confidential information (very frequently authentication credentials) that can later be used by an attacker. Phishing is essentially a form of information gathering or "fishing" for information.
Do not follow any links that you receive within your e-mails and certainly do not input any login credentials on the page that they take you too. Instead, call your Bank, PayPal, eBay, etc., and inquire about the problem. A safe practice would also be to type the URL of your bank in the browser directly and only then log in. Also, never reply to any e-mails that ask you to provide sensitive information of any kind.