The Yuuzhan Vong (ooh-ZAHN vawng) are a race of humanoid sentient beings from the Star Wars universe. They are notable for causing more destruction and chaos than any other antagonist in the Expanded Universe aside from the Empire and the Sith, and for definitely taking the Most Destructive Species crown. And when you consider exactly how much stuff gets destroyed on a regular basis in the EU, that is not a title to be taken lightly.
They made their first appearance in the New Jedi Order series, which is a whopping collection of nineteen novels and twenty-seven stories chronicling the first Yuuzhan Vong War. This series' first installment killed off one of the characters who'd been in Star Wars since the very first movie, which gives you an idea of how the rest of the shebang goes.
As a Species Edit
Yuuzhan Vong (shortened to "Vong" only if you want to be insulting, as using that term alone implies the subject has been cast out of their society) are terrifying-looking. Though humanoid, they stand far taller and weigh much more than any human, and live about three times as long. They have gray skin (rarely, yellow), black hair (if any), no facial expressions as humans use them, and jet black blood. Their nervous system is considerably more sensitive than a human's as well, being designed to feel pain in maximum amounts.
The Yuuzhan Vong, as a species and a society, have evolved over thousands of years to become a vicious, masochistic bunch that treats pain as most other species do pleasure, and in addition one of the most militaristic and aggressive groups ever to appear in the Star Wars Universe. They literally live to ruin people's days. They as a whole have a massive aversion to using technology thanks to their religious beliefs (which glorify sacrifice and death, by the way), and as such all of their equipment, from their armor to their weapons to their spaceships, is organic.
Finally, the Yuuzhan Vong are noteworthy for being, in the words of Jacen Solo, "completely outside the Force." The Yuuzhan Vong, and a good chunk of their equipment, literally do not have connections to the Force, which in the Star Wars Universe is a terrifying concept (theologically alone, never mind the military implications). Force-sensitives like Jedi or Sith are unable to sense them through the Force, and Force abilities like mental suggestion, remote manipulation, etc. are unable to affect them directly (though indirectly utilizing the Force still works; you chuck a rock at an Yuuzhan Vong with the Force, the rock's still going to hit him). A powerful telekinetic blast might briefly knock one off balance, and one of the only Force techniques known to have a direct effect is Force Lightning.
As a Plot Device Edit
The Yuuzhan Vong's homeworld was in another galaxy from the Star Wars galaxy; it was destroyed a long, long time before the long, long time ago, turning them into interstellar nomads. Thousands of years of societal alteration and development produced a society with a masochistic love of pain, death, and sacrifice, a massive aversion to any sort of technological equipment, and one of the most elaborately militarized groups ever to show up in the Star Wars Universe. In other words, trouble.
They became notorious in the Star Wars Universe immediately upon their arrival in the galaxy, an action best compared to gatecrashing a party with loaded guns and all of your friends, and then proceeding to kneecap as many people as possible. They went on a rampage of terraforming and outright brutality that resulted in the bloodiest and nastiest war the Post-Yavin Star Wars Universe had ever seen, which eventually resulted in a pyrrhic victory for the Galactic Alliance, the reformation and slow decline of the New Republic, and the slow re-rise to power of the Empire.
Basically, they took a very delicately balanced scale and kicked it as hard as they could.
In the end, the Yuuzhan Vong wound up more reviled in the Star Wars 'verse than the Empire in many places (statistically, the Empire was worse; however, the 'Vong came in at an extremely delicate time in the galaxy's history seemingly to do nothing but ruin everyone's fun, and was anti-everyone instead of simply anti-nonhuman), and the Yuuzhan Vong War (actually, Wars, since there were two) wound up completely changing the course of galactic history—commonly for the worse.
In the PPC Edit
The PPC has made multiple uses of the Yuuzhan Vong's special traits and abilities.
For starters, due to their aversion to technology and their skill with creating organic substitutes via genetic engineering, the Department of Sufficiently Advanced Technology employs an entire division of Yuuzhan Vong "shapers", having them create and maintain biotic versions of PPC equipment, such as the Tracking Bug, for use by those Agents who, for any number of reasons, can't handle (or aren't allowed to handle/be around) artificially created equipment.
In addition, since the Yuuzhan Vong are outside of the Force as mentioned above, the PPC is quite keen on having Yuuzhan Vong agents working the Star Wars beat. Since so many Star Wars Sues are also Jedi or Sith, their being outside the Force gives them a significant edge up against such Sues, which keeps casualty rates low(er).
Despite the restructuring of Star Wars canon and the sidelining of all EU stories to the Legends continuity, the Yuuzhan Vong agents probably still exist.