The word axial can refer to a few different concepts. Broadly, it refers to the horizontal or longitudinal axis of the body. So an axial cut of the brain would be in the middle, horizontally, if you were looking at the brain from the side. In computerized tomagraphy (CT) scans, axial sections are considered the most important scanning vantagepoint as it allows valuable brain areas to be visible.
Axial can also refer to a period of history coined the Axial Age, sometimes called the Axis Age. This occurred broadly from 800-200 BCE and was characterized by a development of complex and philosophical thinking, religious systems, and intellectuality that emerged in various parts of the world. These new intellectual systems developed concurrently often without interaction with each other - this suggests an evolution in thinking in a broad sense instead of just the spread of information.
Axial can also refer to the method in which the fourth edition of the uses to classify different psychological and psychiatric disorders. This was called the multiaxial approach as different disorders are split into different axes. The DSM-V used the following five different dimensions to categorize disorders: Axis I (clinical disorders like depression, anxiety disorders, and bipolar disorder), Axis II (personality disorders and developmental disorders), Axis III (medical conditions like brain injury and disease), Axis IV (psychosocial and environmental conditions), Axis V ( 'Global assessment of functioning' which is a scale that rates the social, work, and mental functioning of individuals). When the DSM-5 was developed the multiaxial system was eliminated.