ELI5 version: A young woman claimed to have been sexually assaulted by a male student at her university. The University and the Police both investigated the claims and found no evidence to support them, so no charges or punishments were brought forth against the male student. If I remember correctly, the same young man was also accused similarly by 2 other young women, and was cleared of wrong doing in both of those cases as well. Someone may need to fact check me on this, as I'm not in a position to be able to look it up at this moment.

In response, the young woman decided to make her senior project a "living art" project in which she carries around the mattress that she claims the assault took place on, signifying the "burden" she and other sexual assault victims carry. This has lead to a great deal of publicity for her, including personal attention on social media from the United States Ambassador to the United Nations, as well as a great deal of bad publicity for the young man.

Though the young woman never named him specifically, his name was made public by others on the internet through deduction.

It was later discovered that she had sent him Facebook messages AND texts after the supposed rape. None of these messages gave any indication any rape or sexual assault had occurred, and in fact most came across as her making further advances towards him (expressing that she fell in love with him and showing interest in more physical encounters). The messages also gave the appearance that he showed no interest in those advances. This has to lead to backlash, it seems to undermine many of her claims and gives a different connotation to the reasoning behind the rape allegation.

The young man is suing the school for it's apathy in the mattress carrying situation, and the damage all of this bad publicity has done to him personally, his reputation, and his future job possibilities.