Edward_Hua, From the Oxford: The symbol æ, which disappeared from the English language in 13th c., was re-introduced in 16th c. in forms derived from Latin words with æ, and (this being the Latin symbolization of Greek αι) Greek words in αι; as ædify, æther. But this æ had only an etymological value, and whenever a word became thoroughly English, the æ or ae was changed into simple e as edify, ether. The æ or ae now remains, only (1) in Greek and Lat. proper names as in Æneas, Cæsar; even these, when familiar, often take e as Judea, Etna; (2) in words belonging to Roman or Gr. Antiquities as ædile, ægis; (3) in scientific or technical terms as ætiology, æstivation, phænogamous, Athenæum; these also when they become popularized take e, as phenomenon, Lyceum, museum, era.

It's from a letter combination: α + ι, to form an ε(e) sound. It may have originally been a dipthong. As well as names and general words, -αι also worked as the plural form for "female" words (words which ended in -α) in Greek.