Audiation is the process of both mentally hearing and understanding music, even when no music is present. In essence, audiation is thinking in music or thinking about music in a way that brain is able to give meaning to the sounds. You could compare this to a skill that many of us possess - that of thinking in words! The reason we can think in words is because our language education and experience has taught us this skill. Similarly, well educated musicians have the ability to audiate.
The term 'audiation' was invented by music psychologist, Edwin Gordon who has written on it extensively. However, Hungarians were using a similar term “inner hearing” well before Gordon published in this field.