What funkyderek wrote is what is expressed in the original Hebrew, without reading foreign concepts (like messianism or "Satan") into the text.
The woman's zr` "seed" is simply her offspring. This is especially clear from 4:25, which looks back to 3:15 by designating Eve's child Seth (from whom Noah and everyone else is descended) as "another seed (zr` 'chr)" that God "has set for me" (sht-ly), cf. 3:15 where God says that "I am setting" ('shyt) enmity between the seeds (zr`) of the woman and the serpent. When referring to people, zr` is usually collectively used to refer to offspring (Exodus 32:13, 1 Kings 2:33, 11:39, Isaiah 1:4, 41:8, 43:5). The serpent's seed (zr`k "your seed" in 3:25) is similarly the serpent's offspring, i.e. the future progeny of this snake. Hence the curse is stating the etiological origin of the enmity or antagonism between humans and snakes (which is not present at all in the Eden narrative earlier in ch. 3, if you haven't noticed).
This means that the serpent is viewed here as an animal which has offspring of its own. Of course, the preceding verse takes the serpent to be an animal, who would be made lower than "all cattle and every beast of the field" and which shall go "upon its belly and eat dust all the days of its life" (v. 14). The messianic protoevangelium interpretation assumes a switch of reference from a literal serpent (used by Satan) to Satan himself between v. 14 and v. 15, but this is not grammatically permissible. Neither is there any indication that the serpent is other than how the text presents it, i.e. as a talking serpent. There is no hint of ventriloquism or agency of another in the text (as there is in Numbers 22:28, for instance).
The contrast between the two "broods" of the serpent and the woman is reminiscent of the contrast in 1 Kings 2:33, in which the word zr` is similarly used in its usual sense of "offspring": "Their blood shall therefore return upon the head of Joab and upon the head of his seed forever, but upon David and upon his seed and upon his house and upon his throne shall there be peace forever". The reference in Genesis 3:15 is not to a specific offspring but to humanity in general (as Eve is "the mother of all living," 3:20), who continue to be victim of snake bite to this day.
The genesis of the messianic interpretation lies first in a post-exilic reading of text that construes the serpent as Satan or a fallen angel (cf. Wisdom 2:24, 1 Enoch 69:6, Life of Adam of Eve 16:3, 3 Baruch 9:7, Genesis Rabbah 22:12, b. Ber. 9b, etc.), and the progeny of the serpent as either an individual (Cain) or the collective generation (genea) of the wicked. Thus we read that "the seducing and beguiling serpent" defiled Eve's "maidenly purity" (4 Maccabees 18:6-11), that Eve "conceived by Sammael the angel of the Lord and she became pregnant and gave birth to Cain" (Targum Ps.-Jonathan Genesis 4:1), that Eve "imbibed from the Evil One" and "conceived of the Devil's seed" (Tertullian, De Patientia 5.15), that Cain "was begotten in adultery for he was the child of the serpent" (Gospel of Philip 6:5-10), that "the serpent came into her and she became pregnant with Cain" (Pirqei de Rabbi Eliezer, 21). There is probably an allusion to this notion in 1 John 3:10-12 which states that Cain "was of the Evil One" and was among "the children of the Devil". The other "seed" was construed to be either the individual Seth (cf. Genesis 4:25, hence the Sethian gnostic focus on Seth as true seed of Eve and the founder of the gnostics), or collectively as the holy generation (genea), i.e. those who keep the commandments of God (cf. Frg. Targums P & VGenesis 3:15). This overall interpretation is foreign to the original text, as can best be seen in the tension between the "your seed (i.e. the serpent's seed)" and "seed of the woman" -- as this interpretation would make the serpent's seed necessarily the offspring of the woman Eve as well.
The crucial element that gave rise to the messianic interpretation however is the (incorrect) use of the masculine pronoun autos "he" in the LXX of Genesis 3:15 instead of the neuter singular "it", and Paul was led similarly to a messianic understanding of the sperma "seed" of Abraham (originally understood collectively) in Galatians 3:16 (cf. Genesis 12:7, 13:15, 24:7). Paul seems to have a protevangelium understanding of Genesis 3:15 in his statement that "the God of peace will soon crush Satan under your feet" (Romans 16:20). While this expression assimilates the serpent to Satan, it interestingly has a dual understanding of the one crushing the head of the serpent in Genesis 3:15: both a collective entity ("your" feet, i.e. the Christian community) and a non-collective entity, i.e. God (who is performing the crushing of Satan through the feet of the collective church). This is not explicitly messianic and the collective presentation of the church accords with the Jewish reading of the text in Frg. Targums P & VGenesis 3:15. A semi-messianic interpretation appears in Revelation 12:1-17, which alludes to Genesis 3:15 in v. 9 and 17. The latter verse attests the Jewish non-messianic understanding of the women's seed (sperma autés "her seed") as those who collectively obey God's commandments, against whom the dragon/Satan wages war. The passage however also depicts the birth of the Messiah in v. 2-5 and describes the dragon as attacking the woman's child specifically. Here the Messiah is portrayed rather directly as the "seed" of the woman who will defeat the dragon (v. 11-12), an interpretation that co-exists with the collective reading of the source text. This dual understanding accords with the perspective of Revelation, which views the Christian community as acting together with Christ, "they overcame him by the blood of the Lamb" (v. 11). This passage also paves the way for the early Christian understanding of Mary as comparable to Eve (cf. Irenaeus, Adversus Haereses 3.22.4, Tertullian, De Carne Christi 17.5), i.e. the "woman" in Genesis 3:15 being viewed as a different woman than Eve, specifically, Mary.