Surrealism is the combination of realistic subject matter with an unrealistic approach to the interaction in the artwork. Whether it would be an irrational composition that urges the mind towards a more creative mindset or an unorthodox positioning of said subject matter to create contrasting and controversial ideas.
Salvador Dali, for example, was part of the avant-garde surrealism art movement and one of the most prominent surrealistic artists because of his ability to experiment and favour new ideas while still obtaining and including many of the elements of a classical composition.
Surrealism stems from dadaism: a mindset where the public had expressed their disgust and disbelief in their government, their surroundings and their reality. Which resulted in the questioning of the reality of said environment. Keeping that mindset in mind, it becomes much easier to understand and explain the value and symbolism of a very symbolic style indeed.
The reason surrealism has attracted me so much, especially in tattooing, is because composition/design wise you have unlimited freedom as to what subject matter you may use together. You can literally do anything with it, keeping aesthetics in mind, of course.
The idea of so much freedom is quite contrasting compared to the technical aspect of tattooing where a good line is a good line and a soft shade will always be aesthetically pleasing This brings a good balance between the very technical, scientific techniques involved and the creative composition that this style allows.