Having followed this mission for some years: The excitement is not so much over what this solar sail, or solar sails of this sort of design, could do but over where this still-infant technology might lead. A fairly cheap and crude solar sail like Lightsail 2, or Japan's IKAROS space craft, could travel around the inner solar system more or less indefinitely, although not spectacularly fast. It could station keep in an orbit or position that is not naturally long-term stable indefinitely, and it this is the application that most near term uses for it focus on: Things like a long term mission holding a position between the Earth and Sun to provide early warning of solar storms that can damage electronics on Earth and satellites near it, or a re-useable asteroid belt surveyor that will, eventually, visit dozens of asteroids.
Looking to where the technology might lead: As Daysman points out a more advanced (and more heat proof) version of a solar sail could do a 'Sun diver' mission that passed very close to the Sun and picked up a huge speed boost by deploying the sail so close to it. Such a mission, IIRC, would still need centuries or more to reach the nearest star, but could dramatically cut travel time to the outer solar system - imagine if NASA's New Horizons mission to Pluto had needed only one year to get there, instead of nearly ten. Probes to study the plasma, magnetic fields, and dust of interstellar space in under ten years would become feasible this way too (the Voyager probes have only just reached this region of space after decades in flight, and aren't that well designed to study it although they're better than nowt), as well a missions to study very distant comet cores out there.
In the long term researchers are considering things like the base line mission of the Project Starshot research and design effort: A very lightweight, very tough and heat proof, sail that is not pushed by the Sun but by an Earth based array of powerful lasers. Such a system would still be far more fuel efficient than any system that carried it's energy source with it, and could accelerate a one-way flyby probe up to interstellar speeds (5% to 20% of lightspeed) and be able to reach the nearest stars, although not stop at them (probably - potential breaking systems are being investigated too) within a few decades to a half century. This would not be the U.S.S Enterprise, it'd be more like an interstellar Sputnik, but it would technically be a true starship, that people alive today might live to see launch. This is way out of our engineering reach at the moment, although the point of Starshot is to identify, seriously and systematically for the first time, what development would be needed and what sort of time frame would be realistic to aim for.
Lastly the real reason to be excited is that the planetary society is a private, non profit, space advocacy group that has succeeded in launching it's own space mission to test an experimental design of engine, on a budget such a group can scrape together - and it's worked. Their success proves how much the miniaturization of in-space technology over the last fifteen years has actually increased the accessibility of space - the quite 'cubesat revolution', that has seen spacecraft no bigger than a fist become a common thing, has broken the back of the idea that space is for only the most ultra wealthy governments and corporations. It's still not cheap, or easy, but a university, a private group, or even a well funded school, can now put things into space.
Anyway, my two cents.
Way out of my league, too. Equations hurt my brain.
