Along with the changing shape of skirts & draping…

…The other main feature of the style change was the introduction of the cuirasse bodice which dipped front and back extending a little over the hips. By 1880 the soft bustle styles of the 1870s had totally disappeared.

See in these fashion plates (left 1875, right 1878) how the bodice goes from sitting on the waist to clinging to the waist plus the hips below.