Why is the President threatening to adjurn Congress?
It boils down to two linked issues: confirmations and recess appointments. Congress has for years (and probably decades -- the practice started under George W Bush IIRC, but even that was not the first use) used pro-forma sessions to block Presidents from making recess appointments while Congress was not in session. Why? Well, the Senate wants to exercise it's power to advise and consent in important positions, and if they go out of session, the President can appoint someone to the position and they lose their ability to block people they don't like -- at least temporarily.
But generally Presidents appoint a lot of people and the Senate, while often slow on confirming them all, usually manages to keep the important ones flowing and the less important positions are filled by "Acting" people. The people in "Acting" roles don't have full authority but do have enough to keep things moving. In short, normally the Senate doesn't have enough time to confirm everyone, but does confirm enough to keep the issue on the back burner.
So what's different now?
There's one particular position the Senate has been refusing to confirm anyone for. That one position is an important one. It's the Director of National Intelligence. Trump recently appointed an Acting Director to that role, after the Senate blocked his nominee Ratcliffe (who eventually withdrew from consideration when it became clear he would not be confirmed).
So what's the big deal here?
The various coup plots against Trump -- the Russia hoax, the Mueller investigation, the Ukraine hoax -- have all originated out of the intelligence community. To investigate the origins of those plots and prosecute those involved, the President needs to have control of the intelligence community. Until the President has an actual Director of National Intelligence, he lacks control of the intelligence agencies, because the "Acting" people don't have the same authority.
Ratcliffe was a member of the House Intelligence Committee, which -- while under Republican control from 2016 to 2018 -- investigated the Russia hoax. Ratcliffe, specifically, is someone who has seen the full intelligence information on that plot. He knows where to look and where the (hopefully only metaphorical) bodies are buried. That's why Trump wants him -- and that's why the Senate intelligence committee absolutely refused to accept him.
Remember, the Senate intelligence committee is absolutely involved in the scandal. They have a lot to hide, both Republicans and Democrats.
Well, the Senate's power to advise and consent is not supposed to be a power to block the President's nominees completely and hamstring the President's agenda. It's been almost 4 years and the President's first term is almost up. If the Senate continues to block Trump's nominees to the DNI position, preventing Trump from assuming full control of the intelligence agencies and revealing the details of the plots against him that originated within those agencies, Trump will undoubtedly respond by declaring Congress to be in adjournment and making recess appointments.