It's what follows Central Intelligence.

Jeffrey Hillier Agency is the business relationship between a broker and the client where the broker is duly assigned to represent the client.

What Michael Setunsky said!  And, I agree with Patricia Kennedy - you definitely need to learn this in school before you are face-to-face with your first customer/client!

Agency is something you need to get very clear about before you start to represent clients.  Laws vary widely from one state to the next, and it's way to complex to address in a Q&A venue.  If they don't teach it right in the real estate school you attend, you will be a lawsuit waiting to happen.  

I certainly could not say it better than Michael Setunsky 

ROFL - Ryan Huggins - Thousand Oaks, CA nailed this one!

Michael Setunsky See his answer.

Very important to know when acting as an Agent

The laws in real estate vary by state.  A simple definition could be:  who represents who in a transaction.  

Study hard.  Take lots of practice tests.  

Get a copy of an agency disclosure for your state and study it carefully!

Others have answered.

Fiduciary relationship between two parties in which one (the 'agent') is under the control of (is obligated to) the other (the 'principal') . The agent is authorized by the principal to perform certain acts, for and on behalf of the principal. The principal is bound by the acts of the agent, performed in carrying out entrusted duties and within the scope of agent's authority. An agency can be created by (1) express agreement, whether oral or written, (2) implication, based on the custom or practice of the trade, or (3) conduct of the principal.

Is this not covered in your text books?

It is common law.

Jeffrey Hillier - the relationship between a licensee and a consumer.

Agency is created by giving fiduciary duties to a client.

It depends on the context.

It's the relationship you have with a client. Most everyone knows about the doctor patient or attorney client relationship. Your relationship with your clients is like those relationships. 

One person or entity acting on behalf of another person or entity.

Study the requiements in your state.