Planet X and Nibiru are slightly different theories although both about an undiscovered plant in the solar system.
Planet X:
Astonomers have known for years that all the outer planets orbits are disrupted and don't follow the exact path they should do. The only mathematical explanaition for their disturbed orbits would be a large planet deep in the outer solar system that is influencing them. They originally thought that planet was Pluto when they discovered it at first but it's way to small to influence them, that's why there's always been the theory of a planet x, which their is evidence of.
Nibiru:
The Sumarians claimed their gods (the annunaki) lived among them and came from a large planet in our solar system called Nibiru. The orbit of the planet is supposed to bring it in to the inner solar system every 3,600 years. Part of the theory is that we are actually living in a binary solar system and that Nibiru is orbiting around a brown dwarf star, which emits hardly any light and is much smaller than our sun. The orbit of the dwarf star brings Nibiru and the other orbiting bodies of that smaller system in to the inner solar system.
One of the interesting things about the Sumarians is that they knew the distance between each of the planets in our solar system and the colour of each, which should have been impossible for them to know. It was only when probes were used in the 70's that it confirmed the Sumarian beliefs. They also knew the Earth was round and orbited the Sun, and they knew of every planet in our solar system, including Pluto, which wasn't even discovered by modern science until 1930.
Another interesting fact is that in the observable universe it's estimated between 50-80% of all star systems are binary or higher, containing 2 or more stars in the system.