Montesquieu's plan sounds very much like how the United States divides its government, and, in fact, it did influence the US Constitution.
The separation of government into three branches with separate powers was one of Montesquieu's lynchpins for securing personal freedom, whether the form of government is monarchial or republican. Without separation of powers, citizens in a realm cannot rest assured of their liberty, Montesquieu argued. Montesquieu based his ideas about separation of powers on Locke's Second Treatise of Government.
Separating power into three realms—those who make the laws, those who interpret/uphold/if necessary modify or stop unjust laws, and those who execute the laws—keeps the three parts of government in check: the legislature, for example, will be stopped by the judicial branch if it tries to pass unjust laws, and the executive branch (in the US represented by the President) cannot act outside of the laws passed by the legislature without risking removal from power. If the judiciary comes up with a strange or unjust interpretation of a law, the legislature can simply modify the law. Thus, if everything is working the way it ought to, each branch keeps the others from becoming tyrannous.