Twitter has urged a password change for all of its users due to a bug that was found in the system that saved plain text passwords to an internal log file in an unprotected state. Users should not be alarmed according to Twitter as it mentions that there has been no breach, and that after an analysis it has concluded that there has been no misuse of the passwords by anyone or any attempts to use them. Despite this, though, changing the password is still a measure that the company is highly recommending, just in case, as it's still possible that information could have been viewed.
Twitter says that it doesn't believe that any information that was saved to the internal log file has been taken off of the system where it was being stored, and that there's also no reason to believe that any information was misused, however it has still removed those unprotected plain text passwords from the system as a first step and precautionary measure.
Some users may feel safe just knowing that Twitter removed the logged information and after hearing that nothing was believed to be compromised, even with Twitter recommending that users update their password information. The fact that this wasn't a breach though is "significantly worse" according to the Co-founder and former CEO of Evernote Phil Libin, who states that there's no reason for companies to ever store plain text passwords at all let alone in an internal log file. Libin also points out that this "took effort" to make the mistake, suggesting that method of handling password information in this way could have been used intentionally. Malicious intent or not, bug or not, it would still be advantageous for users to take what control they have over their own account privacy and ensure that their information is secure. Changing your Twitter account password can be done relatively easily from the app on your mobile device in settings, or from the settings menu on the web.