The roles are:
(1) Chief of State - Chief of state refers to the President as the head of the government. He is the symbol of all the people.
(2) Chief Executive - The role as head of the executive branch of the government.
-constitutionally bound to enforce the acts of Congress, the judgements of federal courts, and treaties signed by the United States
-Appointment Power: President can appoint a government office or position in the executive branch, the federal judiciary, the armed forces, and members of the independent regulatory commissions.
-Article II, Section 2: President has the power to grant reprieves and pardons (postponements or releases) for offenses against the United States except in cases of impeachment.
(3) Chief Administrator - A Chief Administrative officer (CAO) is a top-tier executive who most often reports to the Chief executive officer (CEO). The CAO manages the day-to-day operations of a business and is sometimes referred to as the Chief operating officer.
(4) Chief Diplomat - The President decides what American diplomats and ambassadors shall say to foreign governments. With the help of advisors, the president makes the foreign policy of the United States
(5) Commander in Chief - The role of the United States President as highest ranking officer in the armed forces. The Constitution provides this power, but, through the system of checks and balances, gives Congress the authority to declare war.
(6) Chief Legislator - When Congress does pass bills, the President reviews each bill and decides whether to sign it into law or veto it. A veto is the president's constitutional power to reject a bill passed by Congress that he does not agree with.
(7) Party Chief - In this role, the President helps members of his or her political party get elected or appointed to office. The President campaigns for those members who have supported his or her policies. At the end of a term, the President may campaign for reelection.
(8) Chief Citizen - The President is Chief Citizen. This means the President should represent all of the people of the United States. Citizens expect the President to work for their interests and provide moral leadership.
I hope this answers your question.