According to The International Standard Bible Encyclopedia By Geoffrey W. Bromiley:
Greek othonion (diminutive of othone) refers to a linen cloth or bandage used in preparing a corpse for burial (John 19:40; 20:5-7).
According to biblical and shroud scholar Kim Dreisbach:
In Jn. 19:40, the Fourth Gospeller uses the word othonia [Gk.] (plural) to describe the linen cloths used in the Burial. Othonia, a word of uncertain meaning, but probably best translated as a generic plural for grave clothes. The same word is used by Luke or his scribe in Lk.24:12 what had previously been described as the sindon in Lk. 23:53. Note: vs. l2 (But Peter rose and ran to the tomb, stooping and looking in, he saw the linen cloths (plural) by themselves; and he went home wondering what happened.) does not appear in the most ancient manuscripts, but is added by later ancient authorities.