The primary headword, which has the same or similar glossing in other lexica, is in the accusative plural. Thus it has evidently been extracted from somewhere; and if the glossing is correct, it carried there sense I.2 in LSJ s.v. a)/mpuc.
LSJ's sense I.1 (alluded to in the second part of the present entry) is that of a woman's hairband, usually made from metal, and worn to restrain a complex hair-style from breaking loose forward. It occurs in the description of Andromache's head-dress at Homer, Iliad 22.469 (accusative singular: web address 1). The prefix am(ph)- indicated that its arms rested on the sides of the head. Such a headband is illustrated from Bronze Age Tiryns by Marinatos fig. 3 (p.11), cf. pp. 20-22, and Bielefeld 1-3.
[1] The word is used of horses by Homer (in the compound xrusa/mpuc, Iliad 5.358, 363, 720, 8.382; see chi 554), and the scholia interpret it as referring to the bit. This is indeed a restraint of similar shape to a hair-band, but the word could refer to any other frontal restraint on a horse; cf. LSJ xalino/s. Wiesner takes the xalinoi/ as all the head-straps of a horse, rather than as the bit alone, and regards the ampyx as the frontal strap on the horse's brow that is brought back to the nape of the neck (p. 20). See also on lipara/mpuc, theta 58.