The Fail Whale is an error message that shows up when Twitter is going through heavy usage or maintenance. While it began as an image of a whale carried by orange birds, the Fail Whale has several versions including an ASCII art version.
The text of the Fail Whale error messages vary and go along the lines of "Twitter is over capacity." It also advises users to come back later or check out Twitter Status for the latest updates on downtime issues. Given the social platform's improved stability and services, the Fail Whale no longer appears as often as it used to.