The best source of information I know is a blog by an American/Korean called Ask a Korean. Doing a search in that site for the word 'impeachment' gives quite a few posts about this, with a lot of detail.
The very short version is that President Park (before she was president) came 'under the influence' of a cult leader, Choi Tae-min, who claimed he could talk with Park's dead mother. His daughter, Choi Soon-sil, became a close friend and took as much advantage of that as she could.
I'm not sure about getting people sent to jail, but suing for defamation and getting people fired certainly happened along with an astonishing amount of theft and improper influence. A good place to start is this post (Part 1) and its Part 2.