An agent of insurance, in human resource terminology would be an employee of a firm who sells insurance products by his own company only. He does not deal in insurance products by other companies, such as the broker.
A broker acts as an agent between a buyer and a seller. The services provided by the broker are chargeable to both the buyer and the seller, which might not be the case with agents of insurance, and hence, commission is charged. A broker acts as an agent for multiple companies unlike an agent of insurance who acts as agent for only his own company.
Example: Suppose an individual holds a savings/current account at a large bank. Now the bank would want to enhance the producer-customer relationship with the individual by increasing its share of wallet or share of product portfolio with the individual. If the bank has various insurance products, then an employee would contact the individual in order to sell the insurance product by his own company. This employee here would be the agent of insurance.