The difference between a molecule's "energy" when the lone pairs (e-) are put on the axial or equatorial planes can help you identify the molecule's most stable structure.
A more stable structure would be one with lower "energy" (less e- repulsion)
For example, in
, there are two possible places (orientations) where the lone pair can exist (axial or equatorial)
Here, the axial lone pair strongly repels the e- pairs in the three equatorial bonds.
Or, the equatorial lone pair can sit on the molecule’s equator (plane perpendicular to axis) where it strongly repels e- pairs in the two axial bonds (giving it a see-saw shape)
Because the lone pair only repels two e- pairs in the equatorial position (meaning that it has lower energy compared to the axial position) this orientation is more stable and preferred.