Once it was clear that light was a wave, the obvious question was: what is waving?
Everyone knew sound waves were compression waves in air, and on a windy day the sound would be carried by the wind. Presumably there was some mysterious background material in the Universe, they called it the aether, that played the same role for light. And, the Earth must be moving through the aether, so that would boost the light speed in the wind direction.
This experiment is designed to detect the Earth’s movement by setting up a race between a blip of light going across stream and back, and one going upstream then downstream. The apparatus can be rotated (by touch on the applet) to switch the two laps, which should change who wins. Try it with various speeds of the “aether wind”. (Note: the expected value of aether windspeed, say the velocity of Earth in orbit, is only one ten-thousandth of the speed of light, easily detectable by these guys, but obviously not something we can show here—we're just illustrating the idea! And, we’re neglecting the (small) change in light direction the supposed wind would cause.)
There's a full explanation in my Modern Physics lecture here.