You can read about it here and here. The Deep State is a grouping of some -- not all -- federal agencies, plus some private corporations, mainly in Silicon Valley. It remains in some measure of power, doing what it does, regardless of the outcome of elections. What it does is mainly maintain the boundaries of the Overton Window to exclude from serious consideration anything that falls outside the "Washington Consensus" of neoliberalism in economic policy and neoconservatism in foreign policy.
As for Trump's relationship with it, see here.
As for Trump's relationship with it, see here.