Eta Aquilae is a yellowish star located at a distance of about 880 light years (or 270 pc) [1, 2, 3], although astronomers seem to have had difficulty accurately measuring that distance). The constellation Aquila is supposed to represent an eagle, and, unlike some constellations, it actually looks somewhat like what it's supposed to represent, with the brightest star in the constellation as the head, two more bright stars in a line below the brightest star representing the body and tail of the eagle, and two other bright stars to the left and right of the body that represent the wings. Eta Aquilae is located in the bottom part of the left wing of the constellation.
What's special about Eta Aquilae is that its brightness is variable. Its magnitude changes from 3.5 to 4.3 over a time period of about 7 days and 4 hours [4, 5]. This change in brightness is big enough and short enough that it's possible to look at the constellation over a period of several days and witness the star changing brightness relative to the other stars in the constellation. This is something that you can even try yourself if you have enough patience.
Eta Aquilae was also one of the first stars that was ever identified to periodically change in brightness. The British astronomer Edward Pigott discovered that the star was variable in 1784 [6, 7]. The scientific paper announcing the discovery of Eta Aquilae's variability is so old that many of the s's look like f's and Edward Pigott is referred to as "Edward Pigott, Esquire". Eta Aquilae turned out to be the first star identified as belonging to a new class of variable stars that would later be named Aquilids. No, just kidding. They were named Cepheids after Delta Cephei, which was the second star to be identified as belonging to this class of variable stars [7, 8]. I feel kind of sorry for Eta Aquilae, which really seemed to miss out on a golden opportunity.
Anyway, Cepheids like Eta Aquilae are giant yellow stars several times the mass of the Sun that have evolved past the stage where they fuse hydrogen into helium in their cores [9, 10]. They could be at the stage where they are fusing helium into carbon in their cores or at a point when their cores have filled up with carbon and they are fusing helium into carbon in shells around these cores. What makes them vary in brightness is that their outer atmospheres are unstable and tend to pulse regularly with a period ranging from about a day to several weeks [10, 11]. At the beginning of one of these cycles, the atmosphere might be as compact as possible, but it would also be relatively hot and opaque. This would cause the outer gas layer to expand, but as it expands, it becomes more transparent and cools. When that happens, the outer gas layer contracts, but it then turns opaque and gets hot again, which causes it to expand again. This continues for a very long time while the star is at this stage in its evolution.
What is notably special about Cepheid variables is that their pulsation periods are directly linked to their luminosities [7, 12]. This means that, if someone spots a Cepheid variable somewhere, they can use the pulsation period to estimate how much light the star produces and then compare that to how much light reaches the Earth to estimate the distance to the star. This has been very important for measuring the distances to other galaxies, and it is still the most reliable technique for making such measurements.
So, astronomers these days will spend a lot of time observing a lot of different Cepheid variable stars, but they still pay extra attention to Eta Aquilae. I would like to think that this is because some astronomers feel guilty about how Eta Aquilae missed out on having a class of stars named after itself and are trying to give it some love and attention, but the real reason is because it is one of the closest and brightest Cepheids as seen from Earth, so it is a good target to observe if astronomers want to understand the details of how Cepheids work.
In fact, Eta Aquilae has attracted a lot of attention because astronomers have determined that it might have at least one and possibly more than one star orbiting it. If this is actually the case, astronomers could use measurements of these orbiting stars to estimate the mass of Eta Aquilae, which would be very helpful for creating accurate scientific models of this star as well as other Cepheid stars. However, astronomers have struggled to determine exactly what's happening in the Eta Aquilae star system. Both the Hubble Space Telescope and the Very Large Telescope found a yellowish star to the east that could be in orbit around Eta Aquilae, but not enough measurements have been made to actually show that this other yellow star doesn't actually just lie somewhere in front of or behind Eta Aquilae by chance and doesn't have anything to do with the Cepheid [13, 14]. Meanwhile, a bunch of other observations imply that a much fainter but really hot blue star should be closely orbiting Eta Aquilae [15, 16, 17], but no one has yet found definitive proof that this hot blue star actually exists. In any case, astronomers will be spending much more time looking at Eta Aquilae to try to figure out exactly what's going on in the star system.