Etymologically the headword (here in the neuter nominative/accusative plural; see n. 1 below) means literally "well-woven-alongside" and refers to garments with finer than average borders or fringes, but it quickly comes to be used figuratively to refer to opulent garments in general, and to the rich and noble people who wear them. LSJ (web address 1) states that the term refers specifically to fine purple borders; however, the only unequivocal authority for that is Photius, Lexicon epsilon2282, which seems to be a description of the Roman laticlavium, an ornament to which the headword certainly might refer, but not exclusively (more ambiguously Pollux 7.46.3). Unless Herodian (1.16.3) and Irenaios (1.7.2) are being pleonastic, the sense of the headword can be separate from purple-ness. See also alpha 3460 and beta 30.
[1] = Synagoge epsilon973; Photius, Lexicon epsilon2281; cf. Hesychius epsilon7060, epsilon7061, epsilon7062, Photius epsilon2282, and scholia on Lucian (155.3 and 275.7 Rabe). The headword is perhaps quoted from the Septuagint (Ezekiel 23.12); if so, it is used adverbially.
[2] An approximation of Diogenes Laertius 6.74; cf. delta 1144. On Diogenes of Sinope, see also delta 1141, delta 1143.
[3] Procopius, Secret History 7.11-13 (web address 2), on the ostentatious garments favored among supporters of the Byzantine circus guilds; cf. alpha 3460, eta 490, epsilon 2838, and Kaldellis (33).