"The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people."
- 10th Amendment to the US Constitution (the last of the "Bill of Rights")
When the Constitution was originally drafted, many prominent statesmen including Thomas Jefferson, Samuel Adams, and Patrick Henry (later known as Anti-Federalists) felt that there needed to be some clause in it that would allow the States to retain some of their authority. They felt that without expressly defining this, the Federal government would start to imply or assume powers that it was not granted to by the States or the people of those states. It was this struggle between the powers of a national government vs. more local sovereignties that prompted the colonies to break from the expansive rule of the British government.
The idea is that the laws governing the people should be held close to the people where they know the people's needs and concerns best, and also allow the people themselves to address their grievances. For example, few people speak face-to-face with their US Senator or even the President of the US, whereas those same people are more likely to come face-to-face with the local Mayor or members of the local legislature. If people have a concern locally, they are more apt to go to, say, a local school-board meeting to discuss the proposed measure, while we tend to "proxy" our voices to national lobbyists and PACs which may not agree completely with our own ideas.
Unfortunately in the modern era (possibly as early as the time during prohibition and the Great Depression), the Federal government has been slowly eroding this protection of the powers reserved to the states mostly by the expansivist interpretation of the "Necessary and Proper clause", the "Commerce clause", and the "Supremacy clause". Thus there are many powers that the Federal government has assumed which limits our liberty and creates a stronger centralized government. Federal gun laws, drug laws, marriage laws, medical insurance, etc. all tend to extend outside the framework of the constitution, expanding the powers of the Federal government and restricting the liberty of the states and people. As a result you have states trying to reassert their authority by creating new laws to make a challenge against these Federal laws on the basis of the 10th Amendment. For example, since many of the Federal gun laws use an expansivist view of the commerce clause, several states have adopted laws that would explicitly state on the firearm that it was "Made in {state of manufacture}" so that all commerce of said firearm within that state would fall outside of interstate commerce and thus nullify the Federal authority over any intrastate transactions. Similar statues have been used in states legalizing the medicinal and / or recreational use of marijuana to prevent raids (or to legally challenge such raids after the fact) from Federal DEA busting legal, intrastate commerce.
But what I see as the most unfortunate aspect of this is that so few of the citizens recognize the states' rights to assume the powers that the constitution has not defined for the federal government. All too often you hear people mention things like the national drinking age, the national speed limit (although this isn't heard as much after that law was revoked in 1995), etc. as though the Federal government holds jurisdiction governing those laws. At most in order to comply with the 10th Amendment, the Federal government may not grant funds to the states that don't comply. It's sad that the citizens of a country founded on freedom and person liberty blind themselves to an expansivist federal government that tends to limit our freedoms.