just open up active directory users and computers from administrative tools. double click on the user accounts that can't change the password which will open up user account properties page. click on the account tab. Under account options verify that the user cannot change password box is unchecked. If it is, uncheck it then click ok. close out all windows.
The other area that may have been enabled is in Group Policy. Group Policy has Disable change password for users under user configuration. If domain group policy for a particular OU/group has been set with disable change password applied, then you'll have to disable that. Note: if group policy was used to disable change of password and you disable it default group policy refresh interval is 90 minutes with a + - 30 minute variance. So changes won't take effect immediately.
May take a bit for the changes to take effect due to domain GP refresh interval [default of 90 mint.