Changing your password in Ubuntu is way easier than you may think. There are two ways to do this, and here they are.
Passwords, especially user and root passwords, are of the uppermost importance in the Linux (and UNIX) world. Your passwords identify you to the system, load your preferences, take you to your directories and let you continue your work where you left off. If you need escalated privileges, or if you want to have more privileges, such as making yourself a member of another group, you will need to tell the system that you are authorized to make the relevant changes. To do this, you have to identify yourself correctly to the system, and the system has to make sure that you are allowed to access and make changes as requested.
How to Change Your Password from the Command Line
To change your Ubuntu password from the command line, open up a terminal and issue the command passwd, which will prompt you to enter your present password and the new password. You will be asked to enter your new password twice.
It may also be a good idea to set a root password if you are making a lot of system configuration tweaks (like installing/uninstalling programs from the command line); because there is no default root password for Ubuntu. Although there are some critics against using a root (super user) account, I personally prefer to have a root password so that I can switch to the root account, make my changes/configurations and quit the root account, instead of preceding each command with sudo. If you prefer this option, make sure that you disable the root account login for security purposes.
How to Change Your Password from the Graphical Menu
The second option is to to go to System -> Preferences -> About me, which will present a dialog box to enter your personal information, as seen in the screenshot on the right. Click on the “Change password" button on the top right corner, which will present you with another dialog box to type in your existing password and your new password. Again, you will need to enter your new password twice to make sure that you have not made a typo.
Usernames and passwords may seem trivial if you are working with your own system. However, there is no mercy in the UNIX and Linux (*NIX to be short) world; you are not asked a hundred times if you are sure to make a change: you issue the command and it is executed. In order to save yourself from making important changes mistakenly, you need to know what you are doing with proper privileges.
In *NIX systems, super user is the God of the system, having the rights to destroy everything. If you can imagine what can happen if your password is in another persons hands, pay attention to your passwords; make them strong, keep them safe and change them from time to time.