The three branches of the US federal government have separate powers given to them by the Constitution. This means that each branch plays a different role in passing and carrying out the laws of the United States.
The branch that does the most to pass laws is Congress. Congress is the only body in the US government that has the power to pass laws. However, the executive branch does have some role in this as well. First, the President must generally sign a bill in order for it to become law. He (or someday she) can veto bills in an attempt to prevent them from becoming law. However, passing laws is mainly the province of the legislative branch.
The branch that does the most to carry out the laws is the executive. All of the agencies that carry out laws, from the Internal Revenue Service to the Department of Agriculture, are part of the executive branch. The Congress does have some say in the matter as it sets the budgets for the various departments and can influence how they carry out the laws.
The judicial branch is mainly confined to interpreting the laws. It has no real power to legislate or carry out laws. However, it does get to say what the laws mean, which can be an important part of carrying them out. It can also strike down laws and presidential actions if they are contrary to the Constitution.