It is in reasonable abundance on Earth, but is rare throughout the universe has a whole
Let's start with a note on scale. "The universe as a whole" is bigger than we can even see, for various reasons. The bit we can see has something like 2 trillion galaxies in it. Each galaxy has hundreds of millions of stars in it. The notion that none of those stars have this unobtanium except for Earth is so phenomenally implausible that it just sounds like magical interference.
Let's quietly ignore the "universe" bit for now, though. Thing is, stuff produced in stars and supernovae gets spread around and mixed up quite effectively over time. The material the Solar System is made of isn't that special as there are plenty of nearby stars and star systems formed from the same source. Within the Solar System, the stuff that the Earth is made of isn't that exotic either... anything you can find here, you'll find some of in the rest of the inner Solar System (though maybe not so much in the outer Solar System). This means you could mine the Moon, or Mars, or maybe the asteroids or Mercury and find at least some of the same stuff, unless it was deliberately and magically placed only on Earth and nowhere else.
The material cannot be reasonably synthesized under all known laws of physics
Thing is, stuff that can't be synthesized under the laws of physics can't reasonably exist in the first place. Where could it have come from, if not from a physical process?
There are potentially some exotic things that could form in the early moments of the universe and be impractical to synthesize since then (such as cosmic strings) but they're not really "materials" and they're not really the sorts of things you might find "on" a planet.
the aliens have not wiped out Earth yet is because using nuclear/chemical/biological weapons of mass destruction might make the Earth uninhabitable for a future harvesting operation
It would take remarkably little to render the Earth uninhabitable for humans, but relatively safe for anyone with a little patience or indeed sufficiently high-tech protective equipment or dare I say it robots.
A few hundred tonnes of the right material wrapped around a few nuclear warheads would make a doomsday device that would handily kill most life on the surface of Earth, and leave the survivors without an industrial base to support them. An interstellar civilization could do this pretty easily, and have the wherewithal to detect hidden settlements using a range of techniques to hunt down stragglers.
It is valuable enough for an advance civilization to fight a war over it, but not so valuable that the civilization cannot survive without it.
(Warning: TV Tropes links incoming)
I think it pretty much has to be some kind of artifact, i.e. a constructed object rather than some simple material resource. Presumably it was built by the inevitable precursors, which is why it is of interest to civilizations which are substantially more powerful than our own but not actually powerful enough to replicate the artifact themselves.
Clearly whatever it is must be very tough (because it has survived probably quite a large span of Earth's history, which have involved a lot of big asteroid impacts and volcanic episodes) and potentially hazardous (because something has stopped the aliens cobalt-bombing the Earth into planet-cockroach).
All that remains is for you to think of a type of macguffin that fits neatly into your setting—an ancient AI; a better superluminal drive; the means for inter-universal travel; the answer to life, the universe and everything—and you're away.
Perhaps also consider that the biggest threat to the aliens trying to obtain the artifact will be other aliens. They might also be the biggest threat to the humans, too.