The executive branch influences the functioning of the US government in a number of ways. One obvious way is the veto power. The president has to consent to any law passed by Congress, and can choose to veto, or refuse his approval, to any law that does not meet his approval. Even the threat of a veto can influence legislation. This is an important check on the powers of Congress.
Another way the executive branch can influence government is through the expansive federal bureaucracy. The variety of agencies that comprise the executive branch are really the instruments of federal policy. For example, the Internal Revenue Service implements and enforces tax laws passed by Congress, the Department of Homeland Security carries out anti-terrorism measures (among many other things) and the Federal Bureau of Investigation investigates cases involving violations of federal law.