Cross processing is a darkroom process used to develop colour film either E6 or C41 and processing it in alternative chemicals, so E6 film will be developed using C41 chemicals and C41 will be developed in E6 chemicals. By processing E6 films in C41 chemicals results in a negative image on a colourless base. Processing C41 films in E6 chemicals results in a positive image. Results will vary depending on the type of film used and the colours can be very unusual.
The technique can be applied in camera RAW and produces images with very warm, purplish tones but again this can be altered depending on the look you are trying to achieve and the image used to carry out the process.