What is the difference between groups, accounts, and users? (for Admins)

Terminology is different with every company.  Terms hierarchy:

Groups: 

A group represents an organization that would have one or more accounts. The group might have an administrator, but as a reseller you may want to assume that role for the group.

The administrator email would be the email address that all self-sign up emails would go to, this person needs to be able to log in verify that accounts are in an active state.

Within the group you also set the report type and email, VCard approval, group messaging restrictions, and the logo that should appear in the upper left corner of the product.

Accounts: 

An account represents a MyRepChat number and contains user logins.

When setting up an account it is a best practice to name the account in a way that you can discern it from others that may be within an organization.

If you were to have 50 accounts at the “ABC Financial” organization, and name them all “ABC Financial”, it would be difficult to pick out one from any other within the list.

Users: 

A User represents a person and has a login associated with it. 

There can be multiple users within one account. For example: John is the primary user on an account, but his assistant is also a user on the account. They both belong to the same number, allowing John's assistant to send messages to clients on behalf of John.