There is a difference between Elizabethan and Victorian corsetry.
The Elizabethan variety provides support for the breasts, and is in a vaguely (upside-down) triangular shape, aided by the use of a busk. This creates the heaving cleavage seen in costume dramas, and therefore the illusion of an hourglass figure (emphasised breasts, streamlined waist, hips left alone). It resembles a small piece of body armour.
By contrast, the Victorian corset is a larger and more flexible affair. It tends to cover the body from just above or below the bust down to the hips. Its purpose is to constrict the waist via tight-lacing and therefore create an actual hourglass figure. Unfortunately, it moves the internal organs up or down to create this effect, and it is possible to die from puncturing a major organ on a rib.
Corsetry is popular with goths and BDSM fans, including yours truly.
Corsets should be distinguished from basques, boob tubes and bustiers. None of these actually aim to change your body shape.
The abandonment of corsets was considered a great victory for the feminist movement. Therefore, don't expect your feminist mom to be delighted if her otherwise-liberated daughter starts tight-lacing.