A broker is someone who buys or sells for someone else for a commission. You may go to a real estate company to get a broker to help you buy a house.
In Middle English broker meant "peddler or retailer." Nowadays a broker still sells things — but she's acting as an agent making deals for someone else and collecting a commission for all that work. Used as a verb, broker means to arrange a deal or negotiate. Working for an advisory firm, a broker may convince you to invest in a company — so the broker would broker a business deal.