The yetzer hara, the evil inclination, is the rabbinic name for the impulse in a person toward self-serving desire and transgression. The term is built out of Genesis 6:5 and 8:21, where "the inclination of the thoughts of the human heart" is described as evil from youth, and the rabbis developed it into a standing feature of their moral psychology, paired with the yetzer tov, the good inclination.
What is distinctive in the rabbinic treatment is its refusal to make the yetzer hara simply an enemy. It is created by God and belongs to a creation pronounced very good; the midrash reads "behold, it was very good" as including the evil inclination, on the ground that "were it not for the yetzer hara, no one would build a house, marry, have children or engage in business" (Genesis Rabbah 9:7). A well-known aggadah has the sages capture the inclination toward idolatry and then discover that no egg is laid in the whole land, so that they blind it rather than destroy it (Yoma 69b). The impulse, on this account, is appetite and drive as such, misdirected rather than intrinsically corrupt, and not removable without removing what makes human life go.
The prescribed response is therefore mastery rather than eradication: through Torah study, which the Talmud calls the antidote (Kiddushin 30b), through the discipline of the commandments, and through the exercise of choice, which the tradition consistently affirms a person actually has. The evil inclination is held to be present from the beginning of life and the good inclination to arrive later, at the age of obligation.
This anthropology is the usual point of contrast with Christian doctrines of original sin. Rabbinic Judaism affirms a persistent and universal inclination toward wrongdoing without holding that human nature is fallen, that guilt is inherited, or that a person is unable to choose otherwise. Later ethical literature elaborated the struggle in great detail, the Musar movement made it a programme of self-examination, and Shneur Zalman's Tanya restructured it as two souls, animal and divine, contending for the same body.