"High crimes and misdemeanors" is a the official standard for impeachment of a US president. As I understand, the term is legally a bit vague because it hasn't been tested much. What kind of concrete things that Trump has done would be most likely (legally speaking) to be used to support the case that he has committed "high crimes and misdemeanors" in an argument for impeachment?
While what constitutes "high crimes and misdemeanors" is technically for Congress to decide upon, the following are often cited as the most prominent examples.
Felony Campaign Finance Violation
Michael Cohen was sentenced to federal prison primarily for his involvement in federal campaign finance violation. In court documents for that case, Michael Cohen and someone refereed to as Individual 1 conspired to break federal campaign finance law, which is a felony.
Individual 1 has been identified as none other than Donald J. Trump (document descriptions made that clear, even before congressional testimony).
That makes Donald Trump an unindicted co-conspirator in that case (a opinion in a justice department memo is currently preventing indictment of a sitting president).
~10 Counts of Obstruction of Justice
The redacted Mueller Report turned over evidence for about 10 counts of obstruction of justice. The details of each instance are a bit lengthy for this posting, but you can read about them in the sections of the Mueller Report labeled:
- "Conduct involving FBI Director Comey and Michael Flynn"
- "The President's reaction to the continuing Russia investigation"
- "The President's termination of Comey"
- "The appointment of Special Counsel and efforts to remove him"
- "Efforts to curtail the Special Counsel's investigation"
- "Efforts to prevent public disclosure of evidence"
- "Further efforts to have the Attorney General take control of the investigation"
- "Efforts to have McGahn deny that the President had ordered him to have the Special Counsel removed"
- "Conduct towards Flynn, Manafort, [HOM]"
- "Conduct involving Michael Cohen"
Over 1,000 people who previously served as federal prosecutors (including Republicans) have issued a joint statement that the evidence in Special Counsel Robert Mueller's report is enough to bring charges for multiple counts of felony obstruction of justice, but again that memo stands in the way of indicting a sitting President.
Trump and the Ukraine Government
Details of this are still emerging but an intelligence official recently filed a whistleblower complaint which Inspector General of the Intelligence Community Michael Atkinson deemed credible and of "urgent concern."
Apparently Trump attempted to bribe the Ukrainian government to try to dig up dirt for him on Joe Biden.
It's a little too early to say precisely what crimes were committed here, but this corrupt behavior does have many in Congress talking about impeachment. In the wake of this revelation, a formal impeachment inquiry has been announced, which is the first step in a long road which could lead to an impeachment vote.