Could you please explain for a layman?
This experiment is basically an upgraded version of the double slit experiment. One of the counter-arguments people had to the original experiment was the idea that there was something we were doing physically that was causing the "measurement problem" (i.e. it isn't reality changing because of the conscious observer but rather our measurement tools having a physical effect on the particles when we decide to "look").
So some scientists came up with a way (using prisms) of not measuring which slit the particles go through in real time as they pass through the 2 holes (thus not affecting the particles in any physical way through measurement) but being able to know after the fact based on the design of the experiment which slit the particle passed through 50% of the time. The other 50% they wouldn't be able to tell at all.
What happened was everytime the scientists could tell which slit the particles went through they got a pattern showing the particles behaved like balls going through one slit or the other. Everytime the scientists couldn't tell which slit the particles went through they behaved like waves going through both slits at the same time. So it was purely our knowledge after the fact that determined whether the particles behaved like balls or waves. This experiment proves beyond a reasonable doubt that its our consciousness that creates reality. Not reality creating our consciousness.
Think of it like a video game. When your character has his back turned, the game is not gonna waste computing power rendering that area in the game. However, if your character turns around the computer instantly renders that enviroment. The delayed choice quantum eraser experiment essentially says our reality works the same way. When we look out into the world particles behave as discrete objects. When we aren't looking they are just a fuzzy wave of probabilities.