5.  What are the NLP "Rep" systems?

"Rep" (Representational) Systems are basically the five senses - the main channels through which we collect input from the world around us, process it and store it:

Visual - Seeing
Auditory - Hearing
Kinaesthetic - Our feelings, both physical and emotional
Gustatory - Taste, and
Olfactory - Smell

A person's current rep' system(s), the one(s) they are focused on at any given time, will usually be reflected in their eye movements (eye accessing cues), their choice of words (sensory predicates), their breathing pattern and even, it is said, in their overall posture.

Notes:

It is important to understand that the early notion of "preferred representational systems" (PRSs) certainly featured quite strongly in the early development of NLP; but after further investigation the importance of PRSs was downgraded, sometime around 1979-1980.  In essence this meant that Bandler and Grinder recognized, from firsthand observations, that people tend to shift their focus from one rep' system to another based on the requirements of their context rather than because they have an ongoing preference for one or two rep' systems over the other.

  It is interesting to note that much of the research conducted in the 1980s, research that allegedly 'disproved' NLP [sic], related to various aspects of the PRS concept which Bandler and Grinder had already abandoned.  This is a key weakness of the reviews conducted by Sharpley (1984, 1987) and Heap (1987).

Intellectual or Cerebral is not, as at least one (non-NLP) psychologist has claimed, one of the rep' systems, though it does have a distinct set of non-sensory linguistic patterns associated with it, such as:

"I understand"
"That's something to think about"
"That's a reasonable idea"
and so on.

Auditory Digital is also not one of the five rep systems, though originally there were six rep' systems, and auditory digital was indeed the sixth rep system (see, for example, Lewis and Pucelik's book Demystifying NLP (Pucelik was Bandler's early collaborator in the field of modelling up to, and for a little while after, Bandler started working with John Grinder.))
AuditoryDigital is also known, especially outside NLP circles, as "self talk", and although it may mainly, or even entirely, take place inside your head, it still comes under the heading of auditory.

Recommended reading: Using Your Brain for a Change