In a Unix OS (and in many other other non-unix OS), a user of a computer is required to authenticate themselves so that the OS may track (or account) their use of the computer. This account can be further traced back to the person themselves when the OS is audited.
The Debian-specific tools to add and remove an account are adduser and deluser from the adduser package. These tools act as a front-end to the low level tools and have intelligence to honor Debian specialties. Whenever possible, use them. adduser and deluser most probably don't exist in this form in non-Debian operating systems.
The low level tools used to manage user accounts and passwords that directly interface with the user database are:
Change Password (passwd)
Create an Account (useradd)
Delete an Account (userdel)
Modify an Account's properties (usermod)
Change login shell (chsh)
Change user information (chfn) (fn means "full name")
These tools come with the passwd package and are likely to exist and work on non-Debian systems as well.
If you use non-traditional methods of user account management (including NIS and LDAP), you'll most probably need different tools.