What does Homer mean when he says, "her words had wings"?

In both The Iliad and The Odyssey, Homer uses the phrase "words had wings" all over the place. Here's one quote of many:

Then the shadow of the swift-footed son of Aeacus knew who I was, and with a cry of grief, he spoke to me — his words had wings: "Resourceful Odysseus, Laertes' son and Zeus' child, what a bold man you are!"

(Emphasis mine.)

I assume this is a Greek idiom, but I don't really get it. What does this phrase mean, and how did it come to mean that?

Nobody knows for sure.

The Greek phrase is “ἔπεα πτερόεντα”, and “winged words” is a literal translation. The idiomatic meaning of this expression is not known, and it has spurred considerable debate amongst translators and scholars.

Herbert Jordan, who translated Homer into English, shares some of the issues he encountered on his website. He discusses winged words.

A common school of thought is that “winged words” connote speed in some manner — either emphasizing the spontaneity of the words, or indicating that the words were spoken quickly. This interpretation is found amongst ancient and modern studies¹. George Calhoun contended that winged words were spoken with unusual emotion or intensity. At the other end of the spectrum his student Milman Parry held that the words held no particular meaning and that Homer “uses this phrase just because it is useful, and without thought for any particular meaning which the epithet ‘winged’ might have”. Winged words played an important role in the elaboration of some theories about oral traditions.

Some translators have translated the phrase literally, others have reflected a perceived emotion, yet others ignored these words.

Incidentally, the expression “winged words” has come to mean a phrase that started as a quote but then took a life of its own. The very coining of this usage by Georg Büchmann made “winged words” winged words.

¹ _{F. M. Combellack, Words that Die. The Classical Journal, 1950.}
² _{M. Parry, About Winged Words. The Classical Journal, 1937.}

After translating Homer for 10 years, I've come to believe that winged words connote words of unusual truth, urgency, or import. They usually occur before an action or change of setting, and thus convey the forward motion of the story.

Hermes, the messager of the gods, is perceived as flying like a bird (see his flight to bring a message from Zeus to Calypso in the Odyssey), or "winged", so that when a speech is of very great importance, it is "winged". Another possibility is that initially, these sort of speeches, έπεα, were not called πτερόεντα but πετρόεντα (made of stone), but later on, for metrical reasons,or because people didnt'any more understand the meaning of this very old epithet, or for both reasons, the poets of the time of Homer (8th century BCE) changed it. Dont' forget that Hermes was associated with "stone" (sculptors were called "hermoglyphai", because most of sculptures represented him, the ερμαί) and the name Hermes itself probably meant "stone".

I've always thought that it was a rather beautiful description of how the thoughts of one person reach the thoughts of another through the medium of language. A poetic expedient, perhaps, but a deep one.