cis-1,2-Dimethylcyclohexane
The red methyl group is equatorial and the green methyl group is axial in this conformation. When a ring flip occurs (see the structure below), the red methyl becomes axial and the green methyl becomes equatorial. The cis-stereoisomer always has one methyl axial and one equatorial, so it is less stable than the trans-isomer, which can have both methyl groups equatorial.
The red methyl group is axial and the green methyl group is equatorial in this conformation of cis-1,2-dimethylcyclohexane.
trans-1,2-Dimethylcyclohexane
Both the red methyl group and the green methyl group are equatorial in this conformation of the trans-stereoisomer. The ring-flip conformation (see the structure below) has both groups axial and is much less stable. Because the trans-isomer has the conformation with both methyl groups equatorial, it is more stable than the cis-isomer, which always has one group axial.
Don't get the idea that the trans-isomer is always more stable than the cis-isomer in disubstituted cyclohexanes. This varies with the position of the groups. For example, in the case of 1,3-dimethylcyclohexane, the cis-isomer has the conformation with both methyl groups equatorial and is more stable than the trans-isomer.
Both the red methyl group and the green methyl group are axial in this conformation, which is much less stable than the one above, which has both groups equatorial.