It operates to maintain the legislative powers to the legislative department, executive powers to the executive department, and those which are judicial in character to the judiciary. Through this allocation of powers, the person entrusted shall not be permitted to encroach upon the power confided to the others, but that each shall, by the law of its creation, be limited to the exercise of the powers appropriate to its own department and no other. There must be independence and equity of the several departments.
photo source: http://w4.nkcsd.k12.mo.us/~kcofer/k2_branches.jpg
In essence, the separation of powers means that the making of the laws belongs to Congress, the execution of the laws is to the executive and the settlement of controversies rests in the Judiciary. Each is prevented from invading the domain of the others. The purpose of the separation of powers is to prevent concentration of authority in one department and thereby avoid tyranny.
The separation of powers however should not be interpreted as complete separation and absolute exclusion. The doctrine carries that although the three branches are not subject to the control by either of the others and each is supreme within its own sphere, they are still equal and coordinate. Equal because they all derive their powers from the same common sovereign through the constitution. And coordinate because they cannot simply ignore the acts done by other departments as nugatory and not binding.