She conducted an experiment in a white Christian children class:
she pretended that a scientific study proved that white blue-eyed people were superior to white brown-eyed people.
Then she said she had made a mistake, and that actually brown-eyed people were the superior ones.
And so the children all acted accordingly: the blue-eyed children felt superior to their brown-eyed peers, until the role reversal, when the brown-eyed children started discriminating against the now-inferior blue-eyed.
This experiment was meant to show how it feels to be a black person when you are discriminated against (It also works with women, actually, with any type of oppression). It also showed that prejudices are acquired rather than innate.
In the video linked above, Elliott talks about that experiment, and explain its purpose and its results. You can see in the public that all black people and majority of white women are enjoying her speech, because they know what she is talking about, they experience discrimination on a daily basis.
And you can see the white man next to her being uncomfortable because he is put in front of his contradictions: he knows, thanks to the experiment, that if he were discriminated against, he would be as infuriated as black people (and women) are.
Even if it wasn’t its purpose, Janet Elliott’s experiment also shows the existence of privilege: which is not experiencing discrimination. White children were put in black people’s shoes, and the man on the set is asked to realise that he wouldn’t be fine being in those shoes.
The teacher also talked about another experiment with adults, inspired by Janet Elliott’s (but not conducted by her), but I couldn’t find anything on that matter, so I’ll ask next time for more precisions because I had genuinely mixed up this experiment with Ellliott’s before editing this post.