President Trump is compromised to Russia. Russia knows a lot of secrets about both his business and political dealings which, if revealed by Russia, would/should cost Trump (and his family) politically, financially, and possibly criminally. Here is the briefest, Twitter-friendly overview:
Business. This is just what we know: what is really scary is what we do not know, but Putin does know, which is what he is using as leverage over Trump.
1) Trump Tower in Russia: the Trump Organization has admitted that they were working with the Russian government to build a Trump Tower in Russia up until the election. Then, multiple members of the family and their lawyer, lied to Congress about it. It is not illegal to build things in foreign countries, but this process involved bribing Putin personally with $50 million penthouse.
2) Money Laundering: Eric Trump bragged that Trump Organization got all of its money from Russia. Then it turns out that the Trump Organization bought over $400 million in property in cash from 2006 to 2016. That is weird for two reasons: (1) Trump Organization did not have $400 million in cash (2) Even if it did, interest rates were near 0%, making it INSANE to buy properties in cash if you could leverage for nothing. Most likely answer is that they were laundering money from Russian aligned oligarchs. Maybe Trump and Trump Organization's taxes will answer this question.
1) Trafficking Documents Stolen from Democrats: Trump Campaign Chair, Donald Trump Jr. and Jared Kushner had at least one known meeting with Russian agents, in Trump Tower. Further, the Trump campaign, including Trump Jr., was in contact with Wikileaks, who is responsible for distributing stolen documents for Russia: The Trump campaign was not just talking to Russians, but known Russian operatives that were helping Russia. Not just Trump Jr., but Roger Stone as well.
2) Providing Russia Internal Polling: Trump Campaign Chair provided internal polling to Russia. Regardless of whether or not the polling was good, it is illegal to share polling data with organizations outside of the campaign. It is also illegal to accept help from foreign governments: While it is not a huge portion of the entire presidential campaign budget, Russia presumably used this data to help coordinate its $1.25 million per month contribution (i.e., operation) to help Trump become president.
3) Meetings with Putin: Since become president, Trump has had repeated meetings with Putin, where there were only Russians in the room. These were likely recorded and will be used against him.
Obstruction The crime is really bad, but so is the obstruction. From firing FBI Director Comey, to silly games with Devin Nunes, to ordering his lawyer to lie to Congress, President Trump has undermined our judicial system, Congress, and the media in order to protect himself from investigations into the obvious fact he is compromised to Russia.
Outcome The key goal of Russia since 1945 has been to undermine the tight relationship between Europe and the United States. On that front alone, from: Paris to Iran to NATO to Syria, the Russians have been extremely successful since Donald Trump became President.