The behavior of ionized gases (plasmas) in magnetic fields is quite different from that of the fluids of our everyday experience, such as air and water. That is why we don't understand plasma dynamics nearly as well as we understand ordinary fluid dynamics, even though it seems likely that many useful applications might be found for well-controlled plasmas if only we understood their workings better. The most famous of these hoped-for benefits is the possibility of controlled thermonuclear fusion generators for electricity, which would use a readily available fuel to produce abundant, clean energy. Moreover, closer to home than Jupiter, there are natural phenomena just outside our atmosphere that are plasma processes like the Io plasma torus and which have tangible effects on portions of our infrastructure such as the electrical power grid. To understand these phenomena better, we need to study them directly, of course, but the history of science suggests that understanding a particular topic is frequently aided by also investigating a different one sharing some of the same characteristics.
To improve our understanding of plasmas is important, but studying plasmas is usually quite difficult. Such studies have typically been done by inserting measuring instruments into laboratory or near-Earth space plasmas. But such measurements only tell us what is happening at the one point where the instrument is, not what is going on everywhere else in the three-dimensional plasma region. It is much like studying the weather; taking a temperature or barometer reading in one place does not allow one to predict the weather. Understanding the weather system requires many simultaneous measurements over a large region. Better yet, imaging (and measuring from afar) the entire atmosphere with Earth satellites enables us to find out what is happening to the atmosphere everywhere at once. This is why we can now predict weather much better than we could 20 or 30 years ago.
Thus an important advantage of studying the Io plasma torus is that it glows, and thus may be imaged from afar by telescopes, telling us, in principle, what is going on everywhere at once in the entire space weather system of torus plasma. The torus is one of the few natural plasma systems that can be studied this way, and therefore is an important guide to the workings of plasma physics. Just as Earth satellites show us Earth weather in detail, so do observations of the Io plasma torus show us space plasma weather at Jupiter in detail.
Moreover, the torus is a fairly close analog of some near-Earth plasma, so studying the torus helps us understand the space weather of plasma held near the Earth by our own magnetic field. (Also, studying Earth plasmas helps us understand the torus) This is important because near-Earth space weather affects our infrastructure.