From The Collaborative International Dictionary of English v.0.48:
Wad \Wad\, v. t. [imp. & p. p. Waded; p. pr. & vb. n. Wadding.] [1913 Webster] 1. To form into a mass, or wad, or into wadding; as, to wad tow or cotton. [1913 Webster]
2. To insert or crowd a wad into; as, to wad a gun; also, to stuff or line with some soft substance, or wadding, like cotton; as, to wad a cloak. [1913 Webster] Wad
From The Collaborative International Dictionary of English v.0.48:
Wadding \Wad"ding\, n. [See Wad a little mass.] [1913 Webster] 1. A wad, or the materials for wads; any pliable substance of which wads may be made. [1913 Webster]
2. Any soft stuff of loose texture, used for stuffing or padding garments; esp., sheets of carded cotton prepared for the purpose. [1913 Webster]