To me it's just another behavior control/pavlovian/focus grouped buzzword the media propagates. At it's core it is the same thing as "iluminati" but since that one is the province of 4Chan and Reddit idiots, they push this. Why? Simple.
People have a new word to use that makes them sound 'in the know' and intelligent to the non politically aware and gives them their daily feelgood to use. Because high school never ends and new things impress small minds. Second, it gives the powers that be an easy identifier for people too stupid to think before they speak, thus saving them time seeking out the easily manipulated to market to. Think of how many buzzwords originate on The View.
"Deep State" is actually a pretty good shorthand to describe the problem. My understanding is that the term came from Turkey, where it had been used for years to describe the entrenched bureaucracy which actually controlled the government.
In our case, "Deep State" is not completely accurate. So far as I can tell, to create a better description of what is happening in our system, we need to combine "Deep State" and "Crony Capitalism" into some sort of amalgamated term.
We have the entrenched bureaucracy as only part of the problem. The other part of the problem is the influence of some extremely wealthy heads of industries and their influence with those same entrenched bureaucrats.
Basically a "good old boy" system that is effectively hidden from the rest of us participants in what we think is a Democratic Republic.