Axial substituents are the positions on a chair conformation of cyclohexane in which the bond to the ring is perpendicular to the average plane of the ring (i.e. pointing up and down towards the poles). When drawing a cyclohexane ring, start with the chair (including the backrest and footrest). Then, starting with the top point of the backrest, draw axial bonds up and down in an alternating manner. Starting at the top of the backrest again, draw an equatorial bond down and out, followed by up and out, etc. On any given carbon in the ring, the axial and equatorial bonds will either be up and down or down and up.
When deciding which chair conformation of a substituted cyclohexane is most stable, try to avoid having large substituents in axial positions, where 1,3-diaxial interactions can occur. This interaction with other axial atoms or groups increases torsional strain significantly. In other words, the chair conformation with the largest group equatorial will be the most stable. A chair flip can convert axial substituents into equatorial substituents and vice versa.