That branch of goverment whose function is to enact laws. Under the United States Constitution, this power is given to Congress. The powers of Congress are limited to those contained in Aritcle I, Section 8 of the Constitution. Among these powers are the power to tax, the power to regulate interstate and foreign commerce, and the power to declare war, among others.
The legislative branch of government in the United States is limited by the separation of powers among the other branches of government. For example, the Executive branch headed by the President of the United States has the power veto legislation. The Judicial branch also maintains a check on the power of the legislature called judicial review, in which legislation is examined to ensure its compatability with the Constitution. Legislation found to be incompatible is struck down.
Compare this system of checks and balances with the system in the United Kingdom. There, the executive is the Sovereign, who is essentially a figurehead with no power of veto. The Prime Minister, generally regarded as being the real authority in the UK, is himself or herself a member of Parliament, which is the legislature. The judiciary in the UK lacks the power of judicial review. There is no check on the power of the legislature in the UK. As a result, the legislature is not really a branch of government, but the government itself.