There is a rather conclusive answer for the one who accepts the New Testament as authoritative interpretation/Jewish understanding of the time.
First, let's deal with the Hebrew.
Genesis 3:15 (WLC)
ואיבה ׀ אשית בינך ובין האשה ובין זרעך ובין זרעה הוא ישופך ראש ואתה תשופנו עקב
This corresponds to the following:
And I will set enmity between you and the woman, and between your seed [זרעך] and her seed [זרעה]: the same [הוא] shall strike your head, and/while you shall strike the heel thereof [תשופנ].
The reason this is often translated 'he' is actually very misleading. The only reason this is translated 'he' is not because there is only one specific person in mind, but because the grammatical gender of the word for 'seed' is masculine, and is singular (but again, singular because it is a collective word like 'sand' is collective). (This also demands that the verbs be masculine, but of course again, no explicit singular descendant is indicated.) The meaning of the word, put most neutrally, is progeny.
The Identity of the Seed of the Woman
A somewhat passing but sufficiently overt reference to this appears in Romans 16:20:
Romans 16:20 (DRB) And the God of peace crush Satan under your feet speedily. The grace of our Lord Jesus Christ be with you.
Here the seed might be interpreted as all Christians. You might object, 'but the serpent wasn't viewed as Satan,' except in the New Testament era, it was (cf. Wis 2:24; Rom 5:12).
In Revelation 12 picks up the woman, serpent and seed theme:
Revelation 12 (DRB)
And a great sign appeared in heaven: A woman clothed with the sun, and the moon under her feet, and on her head a crown of twelve stars: 2 And being with child, she cried travailing in birth, and was in pain to be delivered. 3 And there was seen another sign in heaven: and behold a great red dragon, having seven heads, and ten horns: and on his head seven diadems: 4 And his tail drew the third part of the stars of heaven, and cast them to the earth: and the dragon stood before the woman who was ready to be delivered; that, when she should be delivered, he might devour her son. 5 And she brought forth a man child, who was to rule all nations with an iron rod: and her son was taken up to God, and to his throne. 6 And the woman fled into the wilderness, where she had a place prepared by God, that there they should feed her a thousand two hundred sixty days.
7 And there was a great battle in heaven, Michael and his angels fought with the dragon, and the dragon fought and his angels: 8 And they prevailed not, neither was their place found any more in heaven. 9 And that great dragon was cast out, that old serpent, who is called the devil and Satan, who seduceth the whole world; and he was cast unto the earth, and his angels were thrown down with him. 10 And I heard a loud voice in heaven, saying: Now is come salvation, and strength, and the kingdom of our God, and the power of his Christ: because the accuser of our brethren is cast forth, who accused them before our God day and night. 11 And they overcame him by the blood of the Lamb, and by the word of the testimony, and they loved not their lives unto death. 12 Therefore rejoice, O heavens, and you that dwell therein. Woe to the earth, and to the sea, because the devil is come down unto you, having great wrath, knowing that he hath but a short time.
13 And when the dragon saw that he was cast unto the earth, he persecuted the woman, who brought forth the man child: 14 And there were given to the woman two wings of a great eagle, that she might fly into the desert unto her place, where she is nourished for a time and times, and half a time, from the face of the serpent. 15 And the serpent cast out of his mouth after the woman, water as it were a river; that he might cause her to be carried away by the river. 16 And the earth helped the woman, and the earth opened her mouth, and swallowed up the river, which the dragon cast out of his mouth. 17 And the dragon was angry against the woman: and went to make war with the rest of her seed, who keep the commandments of God, and have the testimony of Jesus Christ. 18 And he stood upon the sand of the sea.
It's very clear here that:
- The male child is the Messiah
- The serpent is Satan, the devil
The woman's seed is Christ and his followers
(I argue that if the dragon is one person, then the woman is Mary (Cf. Rev 12:17; Jn 19:27), symbolic overtones notwithstanding, but that's neither here nor there.)
If Wisdom 2:24 is to be believed, which is of course a given for me in whose canon it is revered as the Word of God, then serpent's 'seed' are none other than those who follow him, as those who follow Christ are the woman's seed:
Wisdom 2:23-24 (DRB)
For God created man incorruptible, and to the image of his own likeness he made him. 24 But by the envy of the devil, death came into the world: 25 And they follow him that are of his side.