Properly speaking, a stoikheion (the first of these glosses) is a simple sound, to be distinguised from a gramma (the second of them), the written letter; but the distinction is not always maintained. See LSJ s.v. stoixei=on II.1 (web address 1).
The letter H was used in early Greek alphabets, including that of Attica, for the aspirate (rough breathing). In central Ionic it was sometimes used for the syllable he. As initial psilosis proceeded in eastern Ionic dialects, the letter was no longer recognized as a consonant, but came to represent the open long e vowel sound which had developed from original long a. When the Ionic alphabet was adopted at Athens (officially in 403/2 BC), the letter was used for both inherited long e and long e from long a. What it sounded like may be inferred from its use in representing the bleating of a sheep (beta 250, cf. beta 336). As time went on, the sound of eta succumbed to itacism. In Byzantine and modern Greek, its sound is indistinguishable from that of iota.