Selling Property/Real Estate Agent
Your job as a Real Estate Agent is to assist those helping to buy and sell Real Property, as discussed in Real Estate.
However, there are several forms of agency that you and a person looking to buy or sell Real Estate can enter into.
Buyer's Agency 
In this form of agency, the agent has a fiduciary responsibility to a person or group looking to purchase Real Property.
As an agent, you must faithfully submit all offers proposed by your client, give your client advice to the best of your abilities and never divulge information that may jeopardize your client's bargaining position.
Seller's Agency 
In this form of agency, the agent has a fiduciary responsibility to the seller of the Real Property, basically mirroring the obligations of a Buyer's Agent (not jeopardizing the Seller's bargaining position, notifying the Seller of all offers, marketing the property to prospective buyers, etc.)
Until recently, Seller's Agency was traditionally seen as what a Real Estate Agent "did", basically as little more than a marketing scout.
Often, a Seller will also become a Buyer for a new property when moving from one residence to another, this is sometimes colloquially referred to as a "Double Whammy"
Disclosed Dual Agency 
It is unethical throughout the United States to be both a Buyer's Agent and a Seller's Agent at the same time without notifying both sides, and in some states, it is unethical to do so even when notifying both sides.
However, in the states where it is ethical, which is the majority of them, an agreement where an agent represents both the buyer and the seller is called a Disclosed Dual Agency. In a Disclosed Dual Agency, the Agent's duties become ministerial, and the fiduciary responsibility switches from that of the client to that of making sure the transaction is completed smoothly and neutrally, while not divulging any information that may have been received from prior agency agreements.
When two agents close a deal from the same office, this is also technically a Dual Disclosed Agency since agents in the same office technically have fiduciary responsibilities to all clients contracted from that office, although the clients directly contracted to a certain agent usually have the agent's primary focus.
Under this form of agency, or lack thereof, the person looking to buy or sell Real Estate is known as a customer rather than a client.
With the squeamishness of many people and groups looking to buy or sell Real Property, this is probably the most common form of Agency, despite its name. Non-Agents do not hold any fiduciary responsibility.
Theoretically, Sub Agents, or agents contracted by other agents to do specific tasks in regards to their client for a share of the commission, are lumped in this category.
Common Misconceptions 
Common to contrary belief, not all real estate agents are Realtors, a Realtor is simply a member of the National Association of Realtors, a U.S-wide group of Real Estate agents.
^ Floyd Wickman, "Sweathogs"(referencing incomplete)