Modeling agencies operate as small independent business with no two agencies working the same. A lot depends on the market in which an agency operates and the owner(s) and agency's personnel.
A modeling agency's number one purpose is to find the model work. They work as the model's representative or agent. As an agent they seek and negotiate contracts of employment for the model or talent who is an independent business. For finding the model work, they take a percent of what the model makes. In some states they are considered private employment agencies and must be licensed by the state. That sounds fairly simple and straightforward, but it is amazing how it can vary.

Very important point:
Agency is a group of people and as any company may have high level professional and not very professional or even complete moron. Unfortunately it is a matter of luck. Well known name of agency can't guaranty anything.
For example: Excellent agency in New York doesn't mean that agency with the same name in some other city has the same high level.
Almost anywhere modeling/talent agencies must be licensed and must be bonded, as well. A licensed agency is required to prominently display its license.
You must find out if an agency is licensed and bonded before signing with any agent.

It is very important to understand the difference between modeling/talent agencies and modeling/talent managers. By definition, a modeling/talent agency is anyone who attempts to secure employment for modeling, theater, film, radio, or television work, but does not include the management of the client’s business affairs.

Model/talent managers differ from agencies because managers are in the business of overseeing the careers of their clients. Arranging for employment is only an incidental, or minor, part of the working relationship between manager and client. Thus, managers advise their clients on appearance, style, portfolio layout and direction of their career. Managers generally charge fees ranging from 15% to 20%.

Are models the employees of the modeling agencies?
No! You shall be acting solely and exclusively as an independent contractor. Modeling agencies and managers provide business support services to the models they manage i.e., advertising, public relations, accounting, bookkeeping, invoicing, collections, and legal support in the form of standard contracts.

Very important point:
Agency is not a nursery house or financial company. Starting modeling career you are starting a corporation under your name. And agency is your business partner! Each of you must do your own job in your partnership. Agency is like a bridge between models and clients. A real good agency will guide you and help to avoid a lot of problems in your career.