R Aquarii is a bit... complicated. It's a binary star system, but that's way too simplistic a description. A lot of science publications call it something like a symbiotic binary star system (and I'll explain what that means later), but even that doesn't convey the complete weirdness of what's going on in R Aquarii. So, bear with me as I break this down into a bunch of smaller parts.
The brighter star in the R Aquarii system looks like a very large red star that slowly varies in brightness. It is technically classified as a Mira-type variable star [1], and it is named after the brightest star in this class of stars. The star would have started out its life as a something little larger than the Sun that fused hydrogen into helium in its core, but the star's core filled up with helium a long time ago, and the star would have then gone through a series of evolutionary changes until it reached a point where its core had filled up with carbon and oxygen but where the fusion of hydrogen into helium continues in a shell around that core. Since the star does not have the mass to trigger the fusion of carbon and oxygen into heavier elements in its core, the core is relatively inert. The outer atmospheres of Mira-type variable stars are unstable and pulse, but over relatively long periods of time, and in the case of the brighter star in R Aquarii, it pulsation period lasts 387 days [1]. The star is also physically large; its radius is about 2 Astronomical Units [2, 3], or 2 times the distance from the Earth to the Sun. So, the larger star in R Aquarii would be a scientific target of interest in its own right if it were not in a binary star system.
The other star in this system is a relatively ordinary white dwarf. This is basically a star that started out like the Sun but has passed through a series of evolutionary stages up to the point where its core had become an inert sphere of carbon and oxygen and it had blown away its entire outer atmosphere, just leaving the inert but still hot core.
The distance between the two stars in R Aquarii is somewhere around 10 AU [4], which is similar to the distance from the Sun to Saturn. For Sun-like stars, that separation is large enough that the stars would just orbit each other. In R Aquarii, however, the evolved red star's outer gas layers are so extended that they can be gravitationally stripped away by the white dwarf. This type of phenomenon is called a symbiotic binary star system, and R Aquarii, which is at a distance of about 760 light years (233 pc) [5, 6], is the closest example of such a system [7]. This would be the primary reason that astronomers would study R Aquarii if nothing else was happening in this star system.
However, other things are happening in the R Aquarii star system. The gas falling into the white dwarf forms a disk that gets really hot and that produces a lot of electromagnetic radiation. Additionally a lot of that gas gets so hot that, instead of falling into the white dwarf, it gets blown away from the white dwarf. Magnetic fields direct this material into two jets of gas that emerge above the poles of the white dwarf and travel for distances of 900 AU [7]. Because the white dwarf is moving around in a circle while producing these jets, the jets have a funky helical pattern [4, 7]. These jets are analogous to jets seen in many other different types of astronomical objects, but because the jets in the R Aquarii star system are so close to Earth, they are easier to study in finer detail. This is another of the major reasons why astronomers spend so much time looking at R Aquarii.
And now, to quote the TV infomercial pioneer Ron Popeil, "But wait, there's more!" The stars in R Aquarii are aligned in such a way that, once during their 44 year orbits around each other, the disk of gas falling into the white dwarf eclipses the Mira-type variable star in the system [8]. Observations of these eclipses actually allow astronomers to measure the sizes of these objects. So, for example, using data from the last eclipse observed in 2020, astronomers have determined that the disk of material falling into the white dwarf has a radius of about 5 AU [8]. Since the eclipse only happened relatively recently, I suspect that a lot of astronomers are still analyzing their data and haven't published their results yet, so be on the lookout for more exciting results in the near future.
So, if I were to summarize what R Aquarii is, I would go back to what I said in the beginning. It's complicated. If I were to try to get more specific than that, then I would end up repeating this entire episode.