Masculine accusative singular or (more probably) neuter nominative/accusative singular of the adjective ἐγκάρσιος (LSJ entry at web address 1). Similarly glossed in Hesychius and other lexica; evidently quoted from somewhere -- perhaps Thucydides 6.99.3 and/or 7.4.1, the Athenian cross-wall, ἐγκάρσιον τεῖχος , at the blockade of Syracuse; also 7.7.2 and cf. 2.76.6.
For other contexts see e.g. Aristotle, de mundo 393a28 (of the 'Sicilian' sea, from the perspective of a passage through the Mediterranean) and several times in Galen, of lateral cuts in dissection.
For the etymology cf. kappa 422. (An adjective κάρσιος is confined to lexicography, but note that Etym.Magn. 310.24-27 sees the root as κείρω , I shear.)
For the synonym ἐπικάρσιος see LSJ s.v.