KIC 8462852, commonly known as the more catchy "Tabby's Star" or colloquial "WTF Star," has been garnering a lot of media attention lately. A sun-like star in the constellation Cygnus, Tabby's star has been observed since at least 1890, but only garnered fame, and a catchy name, within the past year. Then-Yale postdoc and current Louisiana State University scientist Tabetha S. Boyajian authored a paper on the star in 2015 titled "Where's the Flux?" detailing work by citizen scientists and Yale researchers on the star. Citizen scientists of the program Planet Hunters flagged the star for further review because of fluctuations in luminosity, which can often signal that a star has planets (as the planet passes in front of the star, it appears dimmer). The fluctuations in Tammy's star, however, could not be accounted for by anything so simple as a planet or 5.
Tabby's star looks different than other stars with planets in several ways. First, it looks like it has a LOT of debris--more than could be accounted for by a solar system. This is pretty common in young stars, which form in clouds of debris, but not in stars close to the age of our sun, which we think Tabby's star is. It could also be explained by something breaking up recently, like a bunch of comets. However, there's another piece to the puzzle: Tabby's star has been dimming slowly for at least a century. For the entire time we've been observing it, Tabby's star has been getting dimmer at a much faster rate than current models can account for. On top of that, in the past 6 months the rate of dimming has accelerated enormously.
Stars do dim over time--their energy is used up and they can't glow as brightly--but none have dimmed as substantially as Tabby's star. Some people have still tried to explain this away with comets, but that answer is unsatisfying. Tabby's star truly defies any model that tries to define it. It's something we've never seen before.
There are some explanations that could explain Tabby's star that are amazing and outlandish and involve...alien life. You may have heard of the "alien megastructure." The idea is that a civilization with great enough technological prowess can harvest all of the energy of their sun. Humans aren't even close to this--we don't even know how to harvest all of the energy of our planet. There are some ideas of how we could harvest the sun, and one of the ideas that's tossed around more often is the Dyson sphere.
A Dyson sphere is basically a big ol' sphere that goes around a star and leeches off it's energy, providing it to the planet. This would block some (but probably not all) of the starlight from travelling into space and, say, be detected by an unassuming planet on the edge of the galaxy. It would also cause the star to dim fairly rapidly over time, as its energy is being leeched faster than is natural. Basically, it would perfectly explain the strange phenomenon we see with Tabby's star.
Of course, this explanation isn't perfect. And this isn't the first time that scientists have found something beyond our current explanation and blamed it on aliens, only to later discover a perfectly rational reason for it. But me? I want to believe.