On this unglossed headword, a feminine noun attested in a wide variety of genres and contexts, see generally LSJ s.v. What occasioned its inclusion in the Suda is impossible to determine without a gloss, but note e.g. several instances in St Paul's Epistles, which generated comment in the NT Catenae.
In Stoic technical usage it means the self-consciousness that the animal has of itself and constitutes the first familiar thing (prw=ton oi)kei=on) to every animal (see Diogenes Laertius 7.85 and Cicero, De finibus 3.16,20-21, quoting the position of the Stoic Chrysippus; see also omicron 601, which reproduces Diogenes Laertius 7. 85-86, although there the Suda text reads su/ndesis instead of sunei/dhsis, like the standard editions of Diogenes Laertius (H.S. Long, M. Marcovich). The issue of self-consciousness of the animal was especially dealt with in Stoicism by the second-century AD Stoic philosopher Hierocles in his Elements of Ethics, although he uses the word sunai/sqhsis meaning the same as sunei/dhsis. The fragments of Hierocles’ treatise have been edited (and translated into Italian with philosophical commentary) by G. Bastianini and A.A. Long, in (1992) 268-451, vol. 1**. On the Stoic Hierocles and the issue of self-consciousness see also the important paper by Isnardi Parente 1989, especially 2203-2214.