The headword is genitive singular of the adjective a)kraifnh/s, extracted from Thucydides: see n. 2 below. (It also appears in the quotation given, in the uncontracted form a)kraifne/os. LSJ entry at web address 1.
[1] Here and in other lexica (references at Photius alpha833 Theodoridis, second part) an otherwise-unattested a)khrofanou=s is given as the etymon of a)kraifnou=s, surely incorrectly. See further, next note.
[2] If we strip out a)khrofanou=s and its etymological addendum, this gloss is the same as the one in the scholia to Thucydides 1.19.1, from where the headword has evidently been extracted.
[3] Aphrodite, born in the sea-foam off Cyprus; cf. kappa 2738.
[4] Greek Anthology 6.191.1-2 (Cornelius Longus), a dedication to Aphrodite by Leonidas; cf. Page (67-69) and another excerpt from this epigram at delta 1549. This epigram is modeled after Greek Anthology 6.300 (Leonidas of Tarentum; cf. alpha 2388, pi 1568, upsilon 570, and psi 35) as is Greek Anthology 6.190 (Gaetulicus; cf. alpha 1234, alphaiota 392, kappa 2665, pi 969, sigma 958, and psi 35).