The default tax rule in the U.S. is that any benefit you receive, in any form, is earned income and taxable.
Layered atop that default rule are a long list of exceptions, which are generally categorized as (1) exemptions and (2) deductions.
If you attend a Ph.D program where the advertised tuition is $30k per year, and you get a tuition waiver (or w'ever it's called), the default tax rule says that you still earned income because you received a benefit. The nominal value of that benefit is $30k, therefore the student would need to pay taxes on that $30k.
Apparently there's an exemption or deduction that excepts tuition waivers from the default rule, meaning such tuition waivers wouldn't be considered taxable income.
As part of the GOP plan to pay for corporate income tax rate cuts, they must discard many kinds of exemptions and deductions to replace lost revenue from the corporate rate cuts.
To those who say that this is a shell game[1], note that if it was just a shell game then the change wouldn't have been made. In other words, there's an expectation that discarding this exclusion will generate more revenue. That revenue would directly come from students and/or universities, one way or another.
Universities could lower tuition, but one reason for the disparity between nominal tuition and effective tuition is that foreign students disproportionately pay the nominal tuition. Reduce nominal tuition and you reduce the foreign subsidy for domestic students. Not only does the effective price of a graduate education go up, but you're likely to see even more foreign students. Depending on which country you hold citizenship, that's either good for your career prospects or bad for your career prospects.
[1] All the news reports make a point of saying that the university "pays" the tuition waiver. It's a distinction without a difference. The student still derives a benefit, and however the university cares to balance its books (e.g. with double-entry accounting) is entirely irrelevant unless there's incredibly esoteric technical requirement to the particular earned income exception. Such esoteric technical requirements are rare since the 1986 reform as the text of modern rules emphasize underlying economic benefits and not accounting practices, as focusing on the latter create more opportunities for gaming the tax code.