The Deep State comes from the dual state concept.
The dual state is namely a combination of the normative state (the rule of law) and the prerogative state (the pure—political or arbitrary—will of those in power). When the dual state becomes expansive and deeply entrenched in the government, the prerogative side becomes the Deep State.
This Deep State is the administrative bureaucracy that operates with administrative laws rather than the legislative criminal law of the land. These are laws or rules, not passed by congress, are created by the hundreds of agencies that the federal government spends more than $4 trillion a year on.
These agencies control Agriculture, the U.S. intelligence community, the environment, transportation, commerce, pharmaceuticals, the work place, taxes, education, labor, housing, energy and of course WAR. It used to be the Department of War before the change to the Department of Defense.
The problem with the Deep State is the historical documented trend towards authoritarian control of a country. This was first demonstrated in pre WWII Germany. It also has been pervasive in Turkey, Israel, South Africa, Russia and other democracies.
The US Deep State abuses its powers of surveillance, policing, jailing, military means, and now, biomedical control. It overthrew governments for more than half the countries in the world in the last century, inspired every single war of the last century, coopted think tanks, adulterated the academy and corrupted the free press.
It has black box budgets for covert ops, third party payments to the military industrial complex and affiliated third party vendors, and the disguised deep state payments masquerading as foreign aid, NGO subsidies, and international organization “contributions.”
The Deep State is responsible for the Tuskegee Experiment, MK-Ultra, Operation Paper clip, Operation Northwoods, Operation Mongoose and Patcon just to name a few scandals (feel free to google if not familiar).
I'm more of a freedom kind of person, so I'm for Trump to dismantle the corrupted parts of the deep state.