This is something that has caused some debate in the past and something that you should be aware of when involved in a real estate transaction. When you hire an agent, that person has an obligation to act in your best interests and protect your information. There is a buyer representation agreement that is signed by the buyer and the brokerage formalizing this relationship. The seller will sign a listing agreement which sets up a similar relationship for the seller and brokerage.
A multiple representation scenario indicates that the brokerage may be representing more than one party in a transaction. You may have heard of an agent "double-ending" a deal. This means that the agent is selling the house but has also brought a buyer to the table to buy the property. That agent is representing both sides of the transaction. A tricky scenario as the agent must not reveal to either party anything about the other sides motivations, purchasing power or any other bit of information that may influence the purchase and sale. It is obviously in the agent's best interest to have that deal come together as the agent would then be entitled to the full commission.
There is concern that an agent might take advantage of scenarios like this one and orchestrate the showings such that only buyers that the agent represents come to see the property and make offers. That is, of course, illegal and unethical and the agent would be in a lot of trouble if that were ever proven to be true.
Multiple representation can also occur when the brokerage represents more than one party in a transaction. In this case, it is the brokerage, not the individual agent, that has the multiple interest in the transaction. For example, both agents (selling and buying) may work for the same brokerage. They work together at the same office so it is conceivable that they could collude with each other, and share secrets about the parties involved.
When you participate in a sale or purchase, your agent should walk you through these scenarios so that you understand what could happen. Again, it is in the best interest of the agent and brokerage to properly represent their clients or face consequences. Ideally it is best if you hire an agent that is not the one selling the house you would like to buy.