After you are done with using your Gmail account, you should make sure that you choose www.Gmail.com Logout. If you are using Gmail on a personal computer there may not be much issue without Gmail Logout, but when you use your Gmail account from a public computer at a library or Internet cafe, you should definitely go for Gmail Sign Out as there is a chance that others might use your account. You have to note that just closing the browser window doesn’t logout from your Gmail account.
To end your Gmail session, click your account photo or email address in the top right corner, and select Sign out. This operation will allow you to logout from Gmail account. In case, if you have forgotten to sign out of another computer, you can sign out of your other session by going to the bottom of your Gmail, clicking Details, then Sign out all other sessions.