The President believes he's committed no crimes, but he's been pushing the boundaries of the laws so long without getting called out for it he no longer knows what a crime is.
He has long kept two sets of books, one for the IRS and one for the banks in order to obtain fraudulent loans and cheat on his taxes. He's also found ways around laws that prohibit discrimination with regards to housing. Laws are nothing to Trump, he considers them things to be found a way around for his own personal agenda. He has engaged in fraud - Trump University anyone? - and other unethical pursuits on a constant basis.
In the impeachment, he seems to be claiming that obstruction of congress and abuse of power are not "real things" that are illegal.
Abuse of Power is codified as against the law under many names. Acting "Under Color of Law" is one of these and is illegal, see TITLE 18, U.S.C., SECTION 242. This includes acts not only done by federal, state, or local officials within the their lawful authority, but also acts done beyond the bounds of that official's lawful authority, if the acts are done while the official is purporting to or pretending to act in the performance of his/her official duties.
Also see: 25 CFR § 11.448 - Abuse of office.
Abuse of power or abuse of authority, in the form of "malfeasance in office" or "official misconduct", is the commission of an unlawful act, done in an official capacity, which affects the performance of official duties. Malfeasance in office is often grounds for a for cause removal of an elected official by statute or recall election.
The President used the power of his office to withhold aid from, and extort, Ukraine for the political favor of announcing an investigation into the Bidens on TV. He never asked for an actual investigation, only that one be announced. Clearly he was never concerned about corruption in general, contrary to his claims. His clear goal was to obtain a personal political favor, and a thing of much value to him, in exchange for Aid to Ukraine, a thing of great value to Ukraine.
It is also clear that the only thing that stopped this from actually happening is word of the whistleblower complaint and the discovery of the conspiracy. And no, we don't have to wait for the conspiracy to be fruitful in it's goals to be a crime. We arrest terrorists for conspiracy to commit crimes all the time, we don't have to wait for them to actually blow something up.
As for Obstruction of Congress or Contempt of Congress it is clearly a crime
See
https://fas.org/sgp/crs/misc/RL34304.pdfIn this case Obstruction of Congress has been generally applied to the refusal of Trump to comply with (and rather to obstruct) subpoenas issued by Congress seeking to compel either testimony or the production of requested documents.
Trump has cited executive privilege (that has already been decided by the courts to not exist) in his willful Obstruction of a Congressional investigation.
Impeachment is the remedy written into the US Constitution for removing the President "upon a determination that such officers have engaged in treason, bribery, or other high crimes and misdemeanors." I believe it applies to Trump for these crimes.