Long story short, photons (and solar wind) impart a small amount of momentum on the sail. This can be used instead of rockets - as long as you don't mind it taking an absurd amount of time to get you anywhere, that is. And its a whole lot lighter.
An absurd amount of time can be a workable tradeoff depending on the purpose of the mission.
Historically, both thrust and delta-V have been sorely constrained on spacecraft. This is trading a lot of thrust for an infinite* amount of dV, which is a really valuable trade.
(*Practically infinite. It runs out when the sun stops giving solar pressure ;) ).
I am well aware of the potential advantages of solar sails for many things.
I'm just saying they aren't the be-all and end-all. There are many things where they aren't particularly useful (for instance: anything time-constrained. Or anything that requires largeish maneuvers to be done in the outer solar system. And there are certain maneuvers that are... difficult... with a solar sail.)
Also, it's not infinite, nowhere near. Among other things, solar radiation and solar wind will degrade the sail over time. Especially with a lot of the materials they suggest using (mylar, etc.)
Technically, it's as long as you don't mind taking an absurdly long time accelerating. If you're traveling an absurdly long distance, then absurdly slow, but constant, acceleration can actually get you there quicker than chemical rockets.
It's mainly targeted at cube sats, which are very small satellites with usually one specific task or purpose. This could open up space even more to smaller teams of scientists.
I don't know where you got the LEO restriction from. All of the Planetary Society pages are clear that this LEO test is a test, and the real deal is above LEO.
It's not a restriction for solar sails. I know that.
But the grandparent comment said "It's mainly targeted at cube sats".
And cubesats tend to be LEO-based. (They tend to be the cheapest thing possible - and its harder to get into a higher orbit. And they tend to be launched parasitically to boot.)
They're hoping to enable cubesats (or at least small sats) to do deep space or planetary missions by proving a low-mass and low-complexity propulsion system.
Long story short, photons (and solar wind) impart a small amount of momentum on the sail. This can be used instead of rockets - as long as you don't mind it taking an absurd amount of time to get you anywhere, that is. And its a whole lot lighter.