"Every 30 minutes, Kepler measures the brightness of 160,000 stars in its field of view (100 square degrees, or approximately as big as your hand at arm's length). The Kepler data processing pipeline intentionally removes long-term trends, because they are hard to separate from instrumental effects and they make the search for planets harder. Once a month though, they download the full frame, so the brightness of every object in the field can be measured. From this data, we can separate the instrumental effects from astrophysical effects by seeing how the brightness of any particular star changes relative to all its neighboring stars."
"Our results show that over the four years KIC 8462852 was observed by Kepler, it steadily dimmed. For the first 2.7 years of the Kepler mission the star faded by about 0.9%. Its brightness then decreased much faster for the next six months, declining by almost 2.5% more, for a total brightness change of around 3%. We haven't yet found any other Kepler stars that faded by that much over the four-year mission, or that decreased by 2.5% in six months."
"We propose in our paper that a cloud of gas and dust from the remnants of a planetesimal after a collision in the outer solar system of this star could explain the 2.5% dip of the star (as it passes along our line of sight). Additionally, if some clumps of matter from this collision were collided into high-eccentricity comet-like orbits, they could explain the flickering from Boyajian et al., but this model doesn't do a nice job of explaining the long-term dimming. Other researchers are working to develop different models to explain what we see, but they're still working on these models and haven't submitted them for publication yet. Broadly speaking, all three effects we observe cannot be explained by any known stellar phenomenon, so it's almost certainly the result of some material along our line of sight passing between us and the star. We just have to figure out what!"