The first curse includes the whole processes of childbearing, from conception to birth. The Hebrew word rendered "conception" in the New King James version (NKJV) includes the entire pregnancy, while "bring forth" can mean both the beginning or end of the birth process. The Revised Standard Version translates these clauses as, "I will greatly multiply your pain in childbearing; in pain you shall bring forth children."
A human female is unique among mammalian creatures in this respect. Animal females generally bear their young without pain and rarely sicken and die during or from the experience. Women, on the other hand, always experience pain and grief throughout their pregnancies—from morning sickness to contractions—and have historically had a very high mortality rate from childbirth. Better nutrition and hygiene have cut the numbers of deaths dramatically, but the pain and grief remain.
Fortunately, God is a God of mercy. He put within the human female the ability to "forget" her pains in childbirth soon thereafter. Jesus Himself mentions this in John 16:21:
A woman, when she is in labor, has sorrow because her hour has come; but as soon as she has given birth to the child, she no longer remembers the anguish, for joy that a human being has been born into the world.
This curse on Eve has a direct relationship with the end of the curse on the serpent, which involves the woman's "seed," both general and specific (Genesis 3:15). We can infer that God intends us to understand that, because of sin, producing "seed" to fight Satan and his seed will be made more difficult. In a spiritual sense, the church, "the mother of us all," endures great hardship in producing children of God.
Thus, the Bible testifies, "the kingdom of heavensuffers violence, and the violent take it by force" (Matthew 11:12), "We must through many tribulations enter the kingdom of God" (Acts 14:22), and "all who desire to live godly in Christ Jesus will suffer persecution" (II Timothy 3:12). Even the sinless Christ, the promised Seed, was "a Man of sorrows and acquainted with grief" (Isaiah 53:3), forced by sin—yet willing—to bear the agonies of human life and death to become the Son of God, the Firstborn among many brethren.