The Time Vortex is the place where the TARDIS travels through. With the Time Vortex, someone could conceivably reach any point in time or space (though the Time Spiral could cause some problems in the trip).
The Time Vortex apparently looks like the title screen on the series, specifically the title for the new series. Native life in time vortex includes the Reapers in Father's Day and the Chronovores in The Time Monster.
