This happens only when there are 5 bonds in atom, like in pcl5.
In equitorial position, we can accomodate 3 bonds, with 120 degree between each bond(trigonal planar position).
In this formation, the bonds are highly stable, as electrons are seperated by a large angle.
When we add 2 more bonds, they allign in axial position. Here , the bonds are just 90 degree far from the equitorial bond pairs.
So ,they are heavily repelled by the equitorial bond pairs. There are 3 equitorial bond pairs, which heavily repels the axial bonds. So, the electrons of bond move farther away to minimize repulsion.
So, axial bonds are longer.