Attic numerals were used by the ancient Greeks, possibly from the 7th century BC. They were also known as Herodianic numerals because they were first described in a 2nd century manuscript by Herodian. They are also known as acrophonic numerals because the symbols derive from the first letters of the words that the symbols represent: five, ten, hundred, thousand and ten thousand. See Greek numerals and acrophony.
The use of Η for 100 reflects the early date of this numbering system: Η (Eta) in the early Attic alphabet represented the sound /h/. In later, "classical" Greek, with the adoption of the Ionic alphabet throughout the majority of Greece, the letter eta had come to represent the long e sound while the rough aspiration was no longer marked. It wasn't until Aristophanes of Byzantium introduced the various accent markings during the Hellenistic period that the spiritus asper began to represent /h/. Thus the word for a hundred would originally have been written ΗEΚΑΤΟΝ, as compared to the now more familiar spelling ἑκατόν. In modern Greek, the /h/ phoneme has disappeared altogether, but this has had no effect on the basic spelling.