Twitter have announced that a bug in their code has caused plain-text passwords to be stored in internal log files.
These log files are only available internally to Twitter, but as a precautionary measure it is recommended to create a new password, and turn on two-factor authentication. You should use a unique password for every service you use online.
Keeping track of unique passwords can be easier using a password manager.
Two-factor authentication (2FA) for Twitter can be enabled by following the steps found their website. 2FA will prevent an attacker using your password to log into your account. The attacker would also require a random code generated with an authenticator app or sent from the service via SMS to successfully log in. I highly recommend turning on 2FA for all accounts that support it.
You can read more about the Twitter bug on their website.