The Paradox machine was a type of technology that was capable of creating a tear in space and time.
The Master used such a machine by cannibalising the Doctor's TARDIS in order to allow his army of Toclafane to invade Earth. The device created a tear in the sky, allowing millions of the sphere-like aliens to attack the planet and its populace. (DW: The Sound of Drums)
The device was designed to prevent a time paradox from occurring. As the Toclafane Human were Humanity from the future, their attacks on their ancestors would normally have meant that they were destroying themselves and thus would have been erased from history. However, the use of the paradox machine prevented such an outcome from happening, allowing the Toclafane to continue their enslavement of their ancestors. The device was destroyed by Captain Jack Harkness. (DW: The Last of the Time Lords)
NOTE
as the TARDS was cappeble of preventing a Paradox aslong as the people creating the paradox stayed inside, the machine may have simply increesed this power so that it could be used outside of the tardis
