What is the purpose of checks and balances and separation of powers in the Constitution?

To prevent one branch of Government from becoming too powerful

That's why the more civilized countries usually divided their government branches into

Legislature : The branch who creates law and policy

Executive : The government branch who executes the law and policy

Judiciary : The government branch who interprets the law and give resolutions in a dispute

Checks and balances were created in order to ensure that each branches of the government (Executive branch, Legislature, Judicial branch) would be able to fulfill its mandate and also to make sure that no branch becomes more powerful than the other. Meanwhile the separation of power was made in order to make sure that each government branch has a unique role in providing solution for the country.