Twitter is suggesting users change their twitter password and also change it from other platforms if the same password was used there. This is because recently twitter found a bug which stored passwords unprotected in logs before encrypting (hashing) it.
Twitter has fixed the bug and deleted all the stored passwords since then. Although Twitter didn’t find any leak or misuse of this password but still recommends changing it as a precaution.
Twitter CTO Parag Agrawal explained what really happened in detail in his blog at twitter which you can read here(blog.twitter.com).
If you’re using the official twitter app then you’ll be prompted with a message asking to change the password.
In case you are not using the official twitter app then I’m sure that there will be the option to change the password in your app setting. If not then you could open twitter in your browser, go to your profile, then setting & privacy and then select the option password, you’ll then be able to set your desired password.