Who are some of the leaders of each branch of government, and what are their duties?

The three branches of the government are the executive branch, judicial branch and legislative branch. Their duties and responsibilities are:
1) Executive Branch: The executive branch is headed by the President in all forms of democracy. The president may be elected directly by the people (US democracy) or by elected representatives of the people (India, etc.). The president is both Head of State and Head of Government in the former system, while in the latter he/she is only the Head of the State; in either case he/she is Commander-in-chief of all the armed forces. The responsibilities of the executive branch include implementing and enforcing laws, appointing the head of various federal agencies, etc. The Prime Minister (if applicable, as in India or UK) and the cabinet carries out the day-to-day operation of the executive branch. These duties also include commanding the armed forces, acting as the state's representative while meeting International powers, etc.
2) Judicial Branch: The judicial branch is headed by a Supreme or Federal Court and also contains other lower courts. The judicial branch is responsible for evaluating the laws formed by the government. Their duties include interpretation of the constitution, review of laws and deciding matters related to the state's affairs.
3) Legislative Branch: The legislative is composed of (at the national level) the senate or parliament and at state levels of state legislatures. Their main responsibility is to make the laws to govern the country. Their duties also include managing the affairs of state including finances, foreign affairs, law and order, approving treaties, etc.