Nothing to do with shrubbery, these are liners or sleeves generally made of rubber that fit around a bolt or bar to support, position and in some instances cushion the part.
In your average car, bushings are used around the pivot bolts that attach the control arms to the chassis. They are also used around sway bars, the links that connect the ends of the sway bar to the control arms, and on the ends of strut rods.
Rubber bushings provide "compliance" in the suspension to help dampen road noise, vibrations and feedback. Hard plastic bushings "firm" up the suspension for improved handling but also increase ride harshness.
Those who have undergone the NCT will have probably come across bushings on their bill of repair.