Wiggly squiggly swirly misty shit, sometimes with dragons in it.
The Time Vortex is a way for the TARDIS to travel through time, getting at a desired point in the vortex results in the TARDIS materialising at the desired location in that time period. When navigating the time vortex, you must be wary of giant floating words, and actor's faces.
Rory and Amy did naughty things in the time vortex, making their baby a Time Lord, because sure, why not.
Clara was also known to have carried a piece of the vortex in her vagina, causing the TARDIS to give Clara daily orgasms.Sometimes, when someone is really bad, they get thrown into the endless hell of the Vortex, such as Salamander, The Rani, The Master, The Timewyrm, and a little boy named Bobby whose paradox was inconvenient to the First Doctor.