ANSWER: The verse in question, which twice mentions someone being bruised, prophetically refers to both Jesus Christ and Satan. You ask a good question as to the symbolism of each wound. Many Bible students, for years, have especially pondered the meaning of Satan's head being bruised. Genesis 3:15 is important because it is Scripture's first Messianic prophecy and its first recorded overall prophecy.
The Bible verse you are asking about is, "And I will put enmity (hostility, hatred) between you and the woman, and between your seed (Satan's spiritual offspring) and her Seed (her offspring); He will bruise your head, and you shall bruise His heel" (Genesis 3:15, HBFV).
The Hebrew word from which we get "bruise" in Genesis 3:15 is shuph (Strong's #H7779). Its literal meaning is to crush or wound something (in this case a heel and a head). The verse in question occurs after Satan's deception of Eve and her and Adam's subsequent sin. God then discovers what has happened and renders his judgment beginning with the animal (who could stand up and speak) possessed and used by Satan to deceive (verse 14).
God's judgment regarding the sin that was committed then shifts. It goes from the animal used as an instrument of deception (Genesis 3:14) to the one (Satan) who initiated and carried out the evil goal of trying to destroy the Lord's greatest creation (verse 15).
Satan is the "you" referenced in Genesis 3:15 while "the woman" is Eve. "Your seed" refers to the angels (now demons) and humans who have believed the devil's lies and align themselves with his rebellion. "Her seed" is recognized by most Bible commentaries as referring directly to Jesus Christ. It can also symbolically represent the Christian church the Lord would establish through his disciples.
The enmity that leads to the "bruising" of Genesis 3 is easy to understand. God's way of life is based on selfless love and the greatest relationship possible among all. Lucifer's way, however, is founded entirely on self-centeredness, competition, hatred and violence. The inevitable and continuing clash between Satan's way and God's comes to a head with each party being "bruised" by the other.
We now come to the meaning of Satan's bruise he brings to "her Seed" in Genesis 3:15. He is prophesied to bruise Jesus' heel, meaning the greatest penalty he would inflict on God's son would only be a temporary "wound" that would be healed. Satan the devil would be allowed to tempt the Lord to sin and to arrange his physical death but nothing more. God heals the bruise he causes by resurrecting his Son from the dead.
Christ, on the other hand, was foretold to bruise (mortally wound or crush) Satan's head. He has completed the first milestone in this goal by destroying the works of the devil through his life and death (1John 3:8, Hebrews 2:14, Revelation 20:10).
The next step in this plan is Jesus' return to earth that will forcibly free humans from the kingdom of evil (see Revelation 19 - 20). Satan's head (influence), after the Millennium, will be completely bruised (or crushed) when he is eradicated in the lake of fire!