You ask an excellent question! In order to answer this, first, you must understand what "federalism" means. In essence, under a federalist system, the state and federal government share power to make laws and provide for the citizenry.
A careful reading of the Constitution reveals that there is no mention of public education anywhere in the document. As a result, some people argue that, thanks to the 10th amendment, the job of providing for public education belongs to the states. (The 10th amendment reserves those powers neither given to the federal government nor denied to the states for the people and/or the states.) However, there is also a clause in the Consitution, known as the "necessary and proper clause" or the "elastic clause" which gives Congress the power to pass any law that is "necessary and proper" for the governing of the people. This is was allows the federal government to pass laws about public education.
So, thanks to the 10th amendment the states are responsible for creating much of the legislation about education in their own states. (Incidentally, this is why different states have different laws about education, including rules about kindrgarten, truancy, and the legal drop-out age.) And, simultaneously, the Congress can pass laws, like the No Child Left Behind Act, which also mandate certain education policies. This is, at is essence, an example of federalism at work.
The U.S. Constitution established our government, based on "Federalism" or the sharing of powers between the states and national government.
No Child Left Behind is federal legislation that is intended to improve education for all students, but provides for state interpretation and implementation. The four pillars of NCLB are based on stronger accountability, more freedom for states, choices for parents and proven educational methods.
The federal legislation imposes requirements on schools, such as yearly accountability, but in return, schools are given more freedom in spending federal funds.
Ideally, the federal legislation mandates proficiency levels for students and subgroups of students and the states and districts are given flexibility in how to achieve their success.
Educational standards and laws used to be only a state power, but when President Bush and Congress created NCLB, Education fell under federal and state power. NCLB shows the growth of our government, which can have its positives and negatives. On one hand, it is definitely a benefit to have every state on the same page and to have all schools be accountable, but on the other hand when education is so standardized it does not leave room for the uniqueness of each state and their demographics.
Education in America has generally been under local and state control. No Child Left Behind is an effort to have federal accountability standards applied to education. Students and schools nationwide are subject to standards decided upon in Washington, D.C. by the federal, rather than state or local governments as has traditionally been the case in the U.S.