Essentially, it's processing a particular kind of film in the wrong chemicals. Typically, you'd shoot on E6 slide film( which is intended to give positive images in the correct colours), and process the film in C-41 chemicals - which are the chemicals intended to process colour negative film - the kind of film you can get processed on the high street and get pictures back in a hour.
You can of course also X-Process the other way around - and process C41 film in E6 chemicals. Both processes are valid, and will provide results.
The big problem is that the results are massively inconsistent, and can vary due to the Brand/Product of Film you're using, due to the degree of over/under exposure you give the film in camera, the temperature you're processing at, and more other reasons than you could shake a processing tank at.
Some films process better than others, I understand that most varietys of Kodak E6 Slide film work well, whereas every frame of Velvia 100 i've x-processed came out looking like berserk mode in the old video game Doom!
Personally, I'd only recommend doing your own cross-processing when
a) you're pretty happy with getting consistent output processing straight C41 and E6 films
b) you've already researched the look of different types of cross processed film, and picked out a couple you like the effect of. Then bought a cheap stock of 'em from ebay that are out of date.
c) your chemicals are pretty much depleted for processing any more films at standard processing, I'm fairly sure that especially with the 1L re-useable colour chemicals home kits the contamination from a couple of x-pro films will skew your colours for future standard processing. I usually keep my depleted chemicals back expressly for "playing about" like this, but I'm really not worried about even getting a hint of consistency in the output from roll to roll :shrug: