When asked to explain what my mathematics is about, I often answer by showing pictures illustrating the behavior of the dynamical systems I study. Non-mathematicians usually respond with interest, at least polite interest but sometimes much more. They often express amazement that my pictures are in any way related to mathematics.
Visualization can be essential even if the object is the purest of mathematics.
But the pictures most definitely contain information of essential interest to mathematicians. They help us to formulate conjectures, which in many cases would be inconceivable without the pictures. Experimentation, again using computer graphics, often can guide us to a proof, from which any computer aspect is totally absent. Finally, in the essential task of communicating our discoveries to others, the computer graphics may be absolutely essential. I remember Lars Ahlfors, in 1982, telling me that in his youth his adviser Ernst Lindel f made him read the memoirs of Fatou and Julia on the iteration of rational functions.