Browsers will sometimes ask a user if they wish to remember the password that they just entered. The browser will then store the password, and automatically enter it whenever the same authentication form is visited. This is a convenience for the user. Additionally some websites will offer custom "remember me" functionality to allow users to persist log ins on a specific client system.
Having the browser store passwords is not only a convenience for end-users, but also for an attacker. If an attacker can gain access to the victim's browser (e.g. through a Cross Site Scripting attack, or through a shared computer), then they can retrieve the stored passwords. It is not uncommon for browsers to store these passwords in an easily retrievable manner, but even if the browser were to store the passwords encrypted and only retrievable through the use of a master password, an attacker could retrieve the password by visiting the target web application's authentication form, entering the victim's username, and letting the browser to enter the password.
Additionally where custom "remember me" functions are put in place weaknesses in how the token is stored on the client PC (for example using base64 encoded credentials as the token) could expose the users passwords. Since early 2014 most major browsers will override any use of autocomplete="off" with regards to password forms and as a result previous checks for this are not required and recommendations should not commonly be given for disabling this feature. However this can still apply to things like secondary secrets which may be stored in the browser inadvertently.
Ensure that no credentials are stored in clear text or are easily retrievable in encoded or encrypted forms in cookies.