This generator makes passphrases using the Diceware wordlist by Arnold G. Reinhold, following instructions that can be found here. It was inspired by this article. You should trust the generator only as much as you trust your browser to generate a random number, as this is used to emulate a dice roll. The Diceware FAQ explicitly says not to use an electronic version (so again, use the generator with caution). To get it really random, use a dice to roll 5 numbers then look them up.
Very simply, each click of 'New Word' will generate 5 numbers between 1 and 6 and combine them into one 5 digit number. Each number (between 11111 and 66666) is associated with a word on the Diceware list. You should use a minimum of 6 words. For extra security use the 'New Special' button to generate a special character (based on 2 rolls) at some point in your passphrase. Any lookups must be 2 or 5 characters long and consist of numbers between 1 and 6. You can click any word to remove it from the displayed passphrase.
Glenn Rempe has forked the GitHub repository and found the time to create a more featured, more secure, really rather excellent Diceware lookup. You can find and use this here and should definitely check it out/bookmark it. (URL: https://www.rempe.us/diceware/).
Lovingly put together by Ben.
All the source for this project is available on GitHub.
Diceware is a trademark of A G Reinhold. The Diceware wordlist is used under the Creative Commons CC-BY 3.0 license - thank you!