KIC 8462852 is a star that was in the news a few years ago due to some irregular, and inexplicable, changes in brightness. It is often called Tabby's star1, but does not yet have a formal name compatible with human speech.
Tabby's star is a F-type main-sequence star2, much akin to Sol in size and intensity. It is in the constellation Cygnus, although it is too dim to see with the naked eye. It is about 1,470 light-years away from us, and is notable only for what surrounds it. We have no clue what surrounds it.
In 2015, it was formally noted that KIC 8462852 shows unusual fluctuations in the starlight reaching us. Astronomers had been looking for fluctuations in light that would indicate exoplanets, but these fluctuations were extreme and irregular. Irregular changes in brightness are odd, as we would usually assume that these changes are due to something orbiting between us and the star (e.g., an exoplanet), and stable orbits are quite regular. Some have suggested that the changes are irregular because they represent thousands of small orbits, e.g., massive swarms of comets or weirdly shaped dust clouds.3 These would have to be unusually dense and oddly distributed, as KIC 8462852 dims by 22%, which is a lot in any case, and especially a lot when you are assuming anything like a random distribution of millions of objects.
This has led some people to suggest that KIC 8462852 has highly irregular changes in heat transport to its photosphere; this would be interesting, because we don't see this in all the other tens of thousands F-type stars we examine for light fluctuations.
This has also led some people to suggest that we may be seeing an alien civilization building a Dyson swarm; this would be interesting for a number of reasons, starting with ALIENS!, but also because the Fermi paradox has been a long-standing mystery. While the Dyson swam hypothesis is undersupported, to say the least, it does have the advantage that we would a priori expect to see some signs of alien life somewhere, and a priori we do not expect to see irregular, complex orbits of this sort appear in nature.
Observations are ongoing, with the star's blog posting updates a few times a year. Dips in brightness greater than 1% are individually named, but so far there have been no other double-digit dips since the first two -- one on March 5, 2011 (15%), and then on February 28, 2013 (22%). The projected third major dip, if this trend had continued, could not be observed due to a malfunction in the Kepler space telescope, but later observations found no dips of this magnitude, and the larger of the dimmings that followed did not match any pattern. A review of past observations, including photographic plates going back over a hundred years, indicate that the star has slowly been becoming dimmer over the years, more so than other stars of its type; however, there is an obvious problem in interpreting a random sample of photos of a randomly flashing star.
Currently, the best guess is either aliens or dust, with most scientists leaning towards dust; they key here is that there is less dimming in the infrared light end of the spectrum, and more in its ultraviolet light. An object larger than gas or dust particles would dim all wavelengths of light equally when passing in front of the star. The irregularity is still a bit of a mystery, with hypotheses of an orbiting brown dwarf and/or the remains planetary destruction helping to explain some of the weirdness.
This is also supported by observations of a few other stars that show irregular fluctuations in brightness. The white dwarf WD 1145+017 appears to be ripping apart a companion planet, causing pretty much the same sort of chaos we see from KIC 8462852, although for WD 1145+017 we have been able to calculate fairly precise orbits for the planetesimals being shredded. Likewise RZ Piscium is a young UX Orionis type variable star that appears to have decided to eat its planets; while we have not been able to plot the destruction as well as with WD 1145+017, the dimmings are consistent with the planets and dust spiraling in towards the sun. It may be that with more observations, we will be able to model some event of this sort to explain all the observation from KIC 8462852.
1. The designation KIC 8462852 comes from The Kepler Input Catalog (KIC), a star catalog listing over 13 million large, shiny objects. It is likely that KIC 8462852 will eventually get a shorter name, perhaps even one involving more letters than numbers, but in the meantime Tabby's star is used, in honor of lead author Tabetha S. Boyajian.
2. This is science speak for being slightly larger and brighter than the sun (the sun is a G-type main-sequence star).
3. Young stars often have circumstellar discs that have uneven distribution, and which cause periodic and sometimes extreme dimming of the star from our viewpoint. The spiffily-named red dwarf EPIC 204278916 shows dimming of 65%, but is quite regular with it.