There are two types, internal and external. Internal- The hedge fund hires a trader to execute orders for other portfolio managers at the firm. Their job is to execute the order and sometimes give fees to outside brokers in exchange for IPO allocations or information. External-hire an outside BD to execute your orders for you. BTIG is big there. Their job is to find liquidity at a fair price and lower market impact of large orders.
An execution trader places trades as per the desire of other people. An execution trader communicates with a network of brokers and handles incoming price requests. He is responsible to get full information and ensure smooth trade execution. He has to maintain long term , sound relationships with the community of brokers and handle conflicts effectively.
An execution trader has to execute all the trades as asked by his clients and get the best possible prices for them. They take care of those trading segments that are hard to automate and where human interference is essential. Execution traders are experienced people and they also, sometimes help portfolio designers by advising them on how to build good portfolios.