Another term for the system of having three branches of government is "separation of powers." Separation of powers is important to our system because it prevents any one part of the government from having too much power and being able to tyrannize us.
With the separation of powers, no branch of government can simply do whatever it wants. To look at a current example, the Congress cannot simply impose spending cuts (even if both houses of Congress were in Republican hands) because the executive branch is in the hands of the Democrats. Similarly, President Obama cannot impose tax increases because the Republicans in Congress would never allow it.
In this way, separation of powers protects us from having any one part of government simply impose their will on us. This makes it harder for the government to agree on anything and thereby makes it harder for it to do anything tyrannical to us.