As has been already noted, it not legally required, but it’s become a norm / expectation among, at least, major-party presidential candidates here for at least three or four decades. I’m too lazy to look up cites, but I suspect it happened on the heels of Watergate, and Nixon’s abuses of power, and the distrust in government which resulted from this.
And, as has been noted, the reason that candidates have been open about their tax returns is a desire to show at least a modicum of transparency to voters, and to demonstrate that they don’t have financial conflicts of interest. It appears very likely that Trump has had absolutely no desire to do this.
Other information about Trump’s businesses that has come out over the years indicate that his personal finances are intimately entwined with those of his numerous businesses. There are widespread beliefs that he hasn’t wanted to release his taxes because either (a) they may indicate that he is not, in fact, as wealthy as he claims to be, and / or (b) because he’s engaged in questionable financial activities, and he doesn’t want to open the floodgates of people poking around further in his finances.
If memory serves, Trump was the only major-party nominee since then who did not release his taxes. It’s just one of a number of norms and traditions in American politics which Trump has decided to ignore.
During the campaign, he regularly dodged the issue, stating, “I’m always under audit, so I can’t release my taxes” (now, there are no IRS regulations stating this, though yeah, maybe his lawyers, or the little voice in his head, were telling him not to release them). And, he kicked that can down the road long enough that the election happened, at which point his spokesmen could say, “the American public doesn’t care about his taxes, it’s a settled issue, stop asking.”
Are Trump’s finances actually on the up and up? Sure, it’s possible, though I find it hard to believe. His evasiveness about the topic does nothing but fuel more speculation about it all.