It's one of the weird things we see in the sky. E. Aurigae is one of a group of stars called "eclipsing variables," which are usually two stars that orbit each other in such a manner that every now and again, one of them gets fully between us and its companion, eclipsing it. When that happens, what may look like one bright star to the unaided eye seems to dim, since we're seeing the light from only one of the two.
But ol' E. Aurigae is different. It dims, all right, but it dims weird. The companion that orbits the star seems to be some kind of disk made up of dark material (astronomers call anything that doesn't emit its own light "dark material," like planets, interstellar dust and Charlie Sheen's brain).
That would be fine, except the eclipse lasts a couple of years and experiments showed its mass is almost the same as the star itself. That means that whatever is circling E. Aurigae is frickin' huge. It's so huge that if it's really some kind of dust cloud it shouldn't have been able to hold together on its own -- certainly not for the nearly 200 years E. Aurigae's eclipses have been observed -- unless there were stars or some other gravitational sources involved. But there's no sign of any stars within the whatever-it-is that's orbiting E. Aurigae.
Although it would be darn cool if it's some kind of technologically advanced civilization that has harnessed the power of gravity, that's unlikely. The current best guess is some kind of disk of gas with a central hole, held in place by perhaps two very dim stars.
Anyway, now E. Aurigae is dimming on schedule, and astronomers are eager to turn some seriously sophisticated instruments like the space-based telescopes and giant devices called interferometers that will measure different kinds of light and radiation it emits and maybe tell us what's hanging around the star. Or who.