Utterly imaginary nonsense made up by people with victim complexes, and those who prey on them.

Remember how right wing rags spent Obama's entire presidency convincing people that he was going to declare himself dictator, ban guns, exterminate whites, and enforce mandatory Islam? Well since we've got a white republican president again who can't be used to scare the gullible into buying Infowars brain pills, they're still using Obama as their punching bag, and this is the latest conspiracy theory being used.

The general gist is that Obama, instead of just being active in politics like he said he was gonna be, is actively fomenting rebellion against trump, by colluding with the CIA, FBI, and his army of literally thousands of paid protestors, and probably Soros, these being his "shadow government". With the end goal being to overthrow trump, put himself back into power, and then totally do all those dictator things he's totally been about to do for eight years but just decided not to for reasons.

In the real world a shadow government, to the best of my understanding, is just the minority party or opposition party of the one currently in power, who would say "the president handled the situation like this, we would have handled it like this, so the public can see both political positions.