A captcha is a test to prevent automated bots from posting on forums or joining various websites. They typically have a garbled word that a human can make out but computer algorithms have difficulty recognizing.
Whenever you see a box with "enter the letters above", and the letters are some crazy characters in random fonts and colors with lines through them, etc... it's a captcha.
Unfortunately, it's a sort of 'cat and mouse' game - spammers are anxious to break the captchas, and are getting better at it... so the puzzles have to get harder and harder over time...
- Lime