"Enumerated powers" have an academic sound to them. It sounds like something you would read about in a history book. Simply put, enumerated powers are those powers specifically delegated to the Congress by the US Constitution. By the way, they are still there.
Article I, Section 8 of the Constitution lists the seventeen powers specifically enumerated to the Constitution. All of these things are important and the government's function in these areas was supposed to be strong, in order to protect the liberties of every American. Some of the things delegated to Congress include standard weights and measures, coining money, post offices and post roads, the protection of intellectual property, and a national defense. Beyond these and a few other very specific items, there was not much for which the federal government was responsible.
So how did new medicines get regulated? How would certain industries be licensed? What about the many other things done today by the federal government, who would do them? Those powers not enumerated to Congress were left to others, as seen in the Tenth Amendment of the Constitution: "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." That word, reserved, speaks of exclusivity. This was not a preferential view of public policy ("it would be better if the states and people took care of these things"), but a mandate (if it is not listed in the US Constitution, it is for the states and the people). The vast majority of regulations that exist in states came into place from states watching the works of one another. With the many states, our country had a vibrant laboratory with new ideas being brought to the surface and each state emulated those laws that worked best.
The ideas behind this system are both simple and profound. The state governments had virtually unlimited powers, but limited amounts of money. It could not "print money" to fund its programs, because only the federal government had the power to do such. On the other hand, the federal government only had 17 enumerated powers and it had no reason to use inflation as a vehicle to fund its programs. This contributed to the value of the US dollar remaining steady from the era of the founding until the early part of the 20th century (during the New Deal we began to devalue our currency to pay for "extra Constitutional" or unconstitutional government programs).
The Founders of this republic believed in the dispersion of power. They did such in order to maximize individual freedom and to protect the power of the states. This unique system helped to limit the amount of money taxpayers spent on programs they disagreed with because on the federal level, all the enumerated powers were beneficial to all. Meanwhile, people had the power and freedom to move from state to state in order to find a government that best suited their needs. That power to "vote with their feet" kept most state government very small.