Eris is a real planet inside our solar system. Not a myth. Not some suddenly-appearing planet made up by crazy people. Some people claim that the planet Nibiru is actually Eris. This is not true.
Eris is a dwarf planet, probably bigger than Pluto. It resides past Neptune, and is known as a trans-Neptunian dwarf planet. It is the farthest known natural body in our solar system. It has one moon, Dysnomia, and the two were discovered in 2005. Eris was originally known as Xena, or Planet X.
Eris played an important role in modern astronomy - it forced scientists to differentiate between a planet and a dwarf planet. Many people were very upset when Pluto got "downgraded" from a planet - but in truth Pluto is still a planet, just a dwarf-planet. This is an important distinction because as we continue to discover more and more objects out in space, each with unique characteristics, we will have to have some way to classify them - just as scientists classify species and rocks and everything else imaginable. Then our human obsession with organizing everything will slowly be fulfilled in the arena of giant rock-like objects in space.
So what is a planet? you ask. Well, a planet orbits the sun, is massive enough for its own gravity to make it round, and has cleared its neighborhood of smaller objects around its orbit. This definition currently only applies to our solar system, but I'm sure eventually they'll expand it to "orbits a star" and then name everything else differently. Dwarf planets orbit the sun, is massive enough that its shape is controlled by gravitational forces, but hasn't cleared the neighborhood. Dwarf planets are like kids that like to play with other kids. Big planets are like grownups that build giant fences around their yard and call the cops if anyone cuts across the grass.
This is photo taken by the Keck telescope in Hawaii:
This is an illustration of what Eris and Dysnomia might look like:
In conclusion, Eris is the first of many (planets, but not necessarily in our solar system). I can't wait to see what else is out there!
Pictures from NASA.