"material used in stuffing, stuffing used to keep a garment in the desired shape," 1828, verbal noun from pad (v.2).
Entries linking to padding
pad v.2
"to stuff with pads or padding, increase the amount of," 1827, from pad (n.). Of writing, "expand by insertion of extraneous matter," 1831; transferred to expense accounts, etc. by 1890. Related: Padded; padding. The idea of a padded cell in an asylum or prison (1862, padded room) is to prevent those inside from injuring themselves by dashing against the walls.