It is not a concrete entity, they are people with a lot of power and influence who control the CIA, the FBI, the judicial system, the arms lobbies, etc.

A very interesting movie where you can see that someone has more power than the president of the USA is Vice, we could consider at the time that Dick Cheney was part of that deep state.

But as such, the deep state is not an organization, but a group of people with a lot of power, more power than politicians, the result of their interactions is the deep state.