As expected, the Supreme Court has ruled against race-conscious admissions practices as had been implemented by Harvard and UNC (and many other selected US colleges and graduate schools), which had been following Supreme Court precedent, now out the window. Here's the important part for applicants, which the Court bottom lines it at the end:
As before, you can still refer to your race and any other aspects of your background in your essays and in the other parts of the application that you (the applicant) control.
Even if the checkboxes go away. (The checkboxes and definitions were created by the Department of Education, not the colleges themselves. And they were always optional for the applicant.)
More likely: the checkbox data will still be collected because the Department of Education wants the data, but the answers will be suppressed in the applications that admissions officers see.
Note that the media headlines are getting it wrong: