Eve is the name of the first woman on the earth as recorded in the Bible in the book of Genesis. It is a common woman's name and in Hebrew is Chavah, derived from the verb to breathe, or the word life.
God made Eve from one of Adam's ribs when he was asleep to be his "help meet" (fit help) and companion. Together she and Adam lived in the Garden of Eden. Eve was approached by the serpent (Satan) and gave in to the serpent's temptation to eat the forbidden fruit. Eve then had Adam do so as well. Both knew they were breaking God's command. As punishment for Eve's sin, women were made subject to men and were forced to endure painful childbirth. Men were also punished and together they were forced out of the garden. This first breaking of God's commandment is the origin of the concept of Original sin.
The term "mitochondrial Eve" is used in evolutionary biology to identify our matrilineal most recent common ancestor. She is believed to have existed some 160,000 years ago on the African continent. See Mitochondria Inheritance.