Whaling is computer fraud aimed at higher level corporate executives, politicians, celebrities, or other high profile individuals. Whaling usually aims to get information like personal or business account passwords through the use of phishing or spear phishing. It is often very targeted to the individual, including their name, company name, job title, or other information specific to that individual. Because of the targeted nature, whaling is a more sophisticated type of phishing and can be harder for individuals to recognize as phishing.
The name "whaling" came from the fact that important people are sometimes called "big fish." A big fish is someone given special treatment due to their status and often is a person that has a lot of money.