These are the systems of our five senses we all use to take in information and understand the world around us: visual, auditory, and kinaesthetic (physical touch and emotional feelings), including its subcategories gustatory (taste) and olfactory (smell). By necessity they take in and create an internal map that more or less approximate the "real" world.
Although we are capable of using all of these systems, one of the VAK (visual, auditory and kinaesthetic) will tend to dominate and be the primary representational system we communicate in, which will be the preferred or default representational system that we go to automatically and speak in. This will be the system or modality that is preferred to take in most of the information about the world. Although one system will be the primary modality, it is important to keep in mind that all systems are used to some degree.
The concept of VAK deals with the ways we like to process information and how we make sense of the world. When you communicate with someone else, you will be using the VAK. Recognition of the primary representational system that someone is using enables you to build rapport, the sense of sameness that occurs when you enter another person's model of the world. Understanding VAK can give you a real communication advantage.