Deep state is mainly a conspiracy theory. If you really want to be generous and consider it a metaphor for the slowly changing bureaucracy of USA and how it resists change not by conscious will but by the byproduct of having elected and appointed workers from the previous governments in position meaning that there is never a moment when a new president can replace everyone in the management and impose his will without opposition or delay and also how the checks and balances of the US laws and constitution put limits to what the government can do.
Like currently there are still people from Obama, Bush or older regimes in the agencies of USA and some may disagree with the current regime on some matters.
But that is a really generous interpretation and really when people talk about it they mean that there is a shadowy group of liberals who oppose Trump. Some see it as a secret organization that rules USA and assasinates everyone who opposes them, others just think that some "librul cucks" are resisting Trump because they are cucks.