The difference is that basically brokers are higher up the ladder. All brokers start as an agent. After so many years (as required by the state’s licensing board) and so many more hours of education, a real estate agent can become a broker.
Brokers can work independent (i.e. self-employed or out of their own office). They can also oversee agents that are affiliated with their company or office.
To start in a real estate career, you will need to get licensed. To get licensed, you will need to take some real estate related classes. You will need to check with your state’s real estate licensing division to see what is required in your state.