An exclusive agency listing allows a real estate agent to list and market your home, which guarantees that agent a commission if the house sells, through any real estate agent or brokerage firm. The exclusive agency listing agreement also allows sellers to seek out buyers on their own, but does not guarantee a commission to the real estate agent for this.
These exclusive agency agreements are not a very popular type of listing. The reason is that there may not be much incentive for agents to spend their money marketing your home. If a seller can come up with their own buyer, then the real estate agent has spent money they cannot earn back through a commission. In addition, it can be too easy for a buyer to go around the real estate agent and negotiate directly with the seller.
If you find a real estate agent that is willing to accept an exclusive agency listing, do not expect too much from them. That agent will probably just place the listing in the Multiple Listing Service and sit around to see if something happens. A prudent real estate agent would never accept an exclusive agency listing and chances are, you probably want a good agent.