The campaign finance violations concern payments Cohen made on Trump's behalf to two women who claim to have had affairs with him: Stephanie Clifford, the adult-film star better known as Stormy Daniels, and Karen McDougal, a former Playboy model. In his guilty plea, Cohen made the striking admission that he issued those payments "at the direction of the candidate," meaning that Trump himself ordered the payments. Moreover, as the New York Times reports, the payments were made "for the principal purpose of influencing the  election."
Here's what experts on election law and campaign finance told Pacific Standard about this development.
Ciara Torres-Spelliscy, Professor of Law, Stetson University College of Law
Michael Cohen's stunning guilty plea included the gobsmacking admission that Mr. Cohen violated federal campaign finance laws in two different ways: (1) He violated the long-standing ban on corporate political contributions under the Tillman Act of 1907 and (2) he violated the personal contribution limits in the Federal Election Campaign Act that restrict how much money an individual can provide to a presidential candidate. He also indicated that candidate Trump was involved with these violations of law. This could open the president to liability.
Michael S. Kang, Professor of Law, Northwestern Pritzker School of Law
Michael Cohen's guilty plea to campaign finance violations has important implications for President Trump. A critical question before today was whether the hush payments Cohen arranged on Trump's behalf were campaign-related, or simply payments they would've made regardless [of] whether Trump was running for office. Today, Cohen reportedly admitted that the payments were campaign related, not personal expenditures. Assuming prosecutors can substantiate this claim, the payments therefore were illegal campaign contributions that exceeded applicable limits and needed to be reported under federal campaign finance law. What's more, Cohen now admits that the payments were made with the coordination and at the direction of a federal candidate, presumably Trump himself. This is a stunning admission. If it's true that Trump knew the payments were campaign-related and actually directed them as Cohen alleges, then Trump too violated campaign finance law.
Mitchell Epner, Former Federal Prosecutor, Now Practicing at Rottenberg Lipman Rich, P.C.
Today's plea allocation by Michael Cohen was astounding when he directly implicated President Trump (the "candidate for federal office") in two counts of campaign finance fraud. This creates criminal exposure for the president. Because the statute of limitations for charges on these facts is five years, and the payments occurred in mid-2016, the case could be brought at any time up to mid-2021. That is after the next inauguration. Because the case could be brought after Donald Trump leaves office, he faces the possibility of being put on trial with the risk of real jail time. I do not know how likely this set of events is. I do know that there is a risk that no president since Richard Nixon has faced.
Erwin Chemerinsky, Law Professor and Dean, University of California–Berkeley
It is quite dramatic and significant that Donald Trump's lawyer has pled guilty to campaign finance violations in connection with the Trump campaign. This raises a real possibility that Trump himself violated federal law and committed a felony.
*Update–August 21st, 2018: This post has been updated to include a statement from Erwin Chemerinsky.