The excellent graphics below (from the New York Times) are examples of just some of the many (500+?) conflicts of interest that President Trump faces.
Trump has given varied explanations for how he will deal with these conflicts of interest, and for the good of the American public he does indeed need to deal with them. He has promised to resign from his companies, but as of January 20, 2017, there is no evidence that he has done so. Resigning from his companies isn’t even enough to solve the problem, however: “Even if Trump hands over his companies to a new trust, the plan fails to solve many of his bigger business conflicts, experts say. Terms of the trust that would insulate the president from the Trump Organization haven’t been made public. Trump’s decision not to divest his assets has also been heavily criticized by several former White House attorneys and ethics chiefs [source].”
Furthermore, Trump has refused to make his tax returns public, breaking with 40 years of precedent. This makes it impossible to assess the full extent of his business dealings.