Because the light traverses regions of lower and higher density (made up mostly of dark matter), we see a gravitational lensing effect. Sources of gravity distort the image behind the "lens". The article describes a strong lensing effect, which is pretty self-evident. By analyzing correlations of galaxy ellipticities we can measure an effect which is only apparent as a statistical effect. You'd expect no intrinsic correlation of the apparent ellipticity between galaxies (because they can be millions of light-years apart), but this so called weak lensing effect does create a correlation. I basically think of it as observing perfect ellipses through slightly obscure glass and deducing from that the exact shape of the glass.
Thanks to Euclid's data, we will be able to create a sort of 3D map of the total matter distribution (dark and baryonic), which will in turn tell us how the universe evolved better than any other probe. We hope to learn more about dark energy in this way.
Minute Physics have a nice video on this: https://youtube.com/watch?v=tmNXKqeUtJM
And just to clarify to GP, the original dust was not in the same plane and the video explains why it ends up in the same plane.
So too with galaxies---which, from a cosmological perspective, are essentially infinitesimal dust.
Well that depends on what your intuition about randomness is, doesn't it?
Flipping a coin is not random, but you can't tell me the answer before it happens.
Similarly, galaxy orientation is not random, but predicting the world we perceive is perhaps not so easy.
If not, the forces that turn some solar systems and galaxies into rotating disks might not act the same at the supergalactic scale in time and space?