The first and main part of this entry is generated by Polybius 6.24.5, on the Roman army of the middle Republic: kai\ to\ me\n me/ros e(/kaston e)ka/lesan kai\ ta/gma kai\ spei=ran kai\ shmai/an, tou\s d' h(gemo/nas kenturi/wnas kai\ tacia/rxous. Converted from Greek military vocabulary into Roman, this becomes: "they called each company ordo and manipulus and signum, and etc.".
The first of the Greek terms there, and again here, is also found as shmei/a, and properly denotes the standard (note the gloss si/gnon=signum in Hesychius sigma493); hence the meaning of military unit serving under the same standard. See also sigma 314.
[1] In this form see e.g. Plutarch, Galba 22.6 (and cf. the semeio- form in e.g. Plutarch, Brutus 43.3, and semaia- in e.g. Polybius 6.24.6; LSJ lists still other forms).