A rogue planet is a planet that either has an extremely elongated orbit around its star so that it is not on the same orbital plane as the other planets in the system, or it is an interstellar planet, a planet that drifts freely through space and doesn't orbit a star at all.
If the orbit is extremely elongated or sharply inclined the planet could take hundreds or thousands of years to make a complete orbit around the system. The strange orbit of a rogue planet may make it undetectable and unknown to an observer on any of the other normally aligned planets in a solar system.
There are many theories on how rogue worlds are created; they could be massive brown dwarfs, or be terrestrial planets that for some reason break free of their solar system orbits and are flung away into space. Some planets orbiting a star may have been captured rogue worlds.
Since most definitions of "planet" describe in some fashion, "an object which orbits a star", the idea of rogue planets casts doubt on the very nature of what a planet is. Some definition concerning origin, such as "an object that formed from a star's accretion disk" would be required to include rogue planets in the same class as the planets in our solar system.
The theory of rogue planets could also account for some of the so called dark matter detected in space.
The planet Nibiru, the "12th planet" in the writings of Zecharia Sitchin, based on his extra-terrestrial interpretation of Sumerian mythology, could be considered a rogue planet, since it supposedly possesses a highly elliptical, 3657-year orbit. However there is no scientific evidence for such a planet and his claims are largely considered pseudoscience.