Typical use case for this is to set the origin of the sprite to its center point.
Something like this:
auto bounds = mySprite.getLocalBounds();
mySprite.setOrigin( bounds.width / 2.f, bounds.heigth / 2.f );
Other use cases is for collision detection between sprites, you need to know about the geometry of the sprite, and therefor can use getLocalBounds().
But in both cases GetTextureRect also serves well:
auto rect = mySprite.GetTextureRect();
mySprite.SetOrigin(rect.width / 2.f, bounds.height / 2.f);
The only difference between these two functions is that GetTextureRect returns an x and y relative to the Texture's coordinates (useful for sprite animation). My curiosity regarding the usage of this method is specifically the returning values of the coordinates of the Sprite.