In 1995 a woman named Nancy Lieder claimed she had been contacted by aliens and warned of an imminent collision between the Earth and another planet named either Nibiru or Planet X. The name Planet X comes from Percival Lowell, the astronomer who suggested an extra planet beyond Neptune (which he nicknamed X for short).
This claim from Nancy Lieder is the sum total of the so-called "Planet X theory". It's really a bad name, because a theory is an idea which has lots of evidence to support it, but Lieder's claim has none. In fact, Lieder's original claim was that the Planet-X collision would take place in 2003...which I'm pretty sure was proven false. There are still some people who claim that the Planet X event is going to happen, but these claims aren't based on any actual data so there's little reason to be alarmed by them. I could just as easily claim that a giant strawberry is headed for Earth. Technically you can't prove that false, so I could refer to it as the Stawberry-event-theory, but there's no reason you'd believe it. So, what is Planet X "theory"? Nothing to worry about.