The Underground Church rejects Beijing's jurisdiction and forms what the government considers to be illegal worship cells. Usually the news if it focuses on the Underground Church tends to report on the Protestant side of things.
However the Catholic Underground is getting a little more attention as of late due to the attempts of Pope Francis to find a means of reconciliation.
His overtures to Beijing are stirring controversy and confusion both in China and the larger Catholic communion.
This article aids in understanding the issues:
On the one hand it's in Rome's interest to make peace with Beijing and bring some stability to the situation. On the other hand, such an agreement risks serious compromise and it's certainly understandable why many Underground Catholics would view this as an impossibility... even a betrayal.
Here's a link to a related post from October 2016: