For one thing, in Genesis, the breath of life, meaning the soul, was infused in Adam after the creation of his earthly body. This suggests, according to rabbinical interpretation, that the human status of the unborn child is not completed since s/he does not have a soul infused into their body. There are other passages in Torah as well that suggest similar differences in the human status of the unborn.
In the Talmud, there is the concept of the rodef (pursuer) that has been applied to abortion in cases where the mother’s life is in danger. The unborn child is, in a sense, pursuing the life of its mother, and can be (in fact, must be, based on Jewish Law) aborted to preserve her life. It’s a complex explanation and should be studied in its entirety in order to be understood. The Talmud also discusses instances of rape and incest as leniencies in which abortion is permitted, but not required.