Much as some users may hate it, having a good password is an important thing. At some computer installations, such as are found in the various alphabet soup agencies in the spy business or in the military, the ``password'' changing program may actually be quite complicated. Typically you don't want any word from the system dictionary as a password, words which are all one case, a word spelled backwards, a name, a name spelled backwards, words with trivial number/letter substitutions ($ for S, etc.). Some places don't even want the password to be pronounceable. Quite often the password is restricted from being either too long or too short.
If you run the passwd program you will be prompted for your old password, and for your new password twice. Having you type it in twice is to make sure you don't make a typing mistake. You are only allowed to change your own password, while the superuser (root) can change anyones password.
Passwords can be applied to groups, as well as user IDs, they can be aged (minimum and maximum lifetimes). Some sites as a matter of policy, will run ``cracking'' programs against their users accounts to ensure good password choice.