1,3 Diaxial interactions occur when the non-hydrogen substituent on a cyclohexane occupies the axial position. This axial substituent is in the eclipsed position with the axial substituents on the 3-carbons relative to itself (there will be two such carbons and thus two 1,3 diaxial interactions). This eclipsed position increases the steric strain on the cyclohexane conformation and the confirmation will shift towards a more energetically favorable equilibrium.
Gauche interactions occur when a non-hydrogen substituent on a cyclohexane occupies the equatorial position. The equatorial substituent is in a staggered position with the 2-carbons relative to itself (there will be two such carbons and thus two 1,2 gauche interactions). This creates a dihedral angle of ~60°. This staggered position is generally preferred to the eclipsed positioning.