Erusin (אירוסין) is the Hebrew term for betrothal. In modern Hebrew, "erusin" means engagement, but this is not the historical meaning of the term, which is the first part of marriage (the second part being nissuin).
Since the Middle Ages it is customary for the marriage to occur immediately after the betrothal, and to perform the betrothal during the marriage ceremony itself. Previously this was not the case, and there were often several months between the two events.
In Hebrew and classical rabbinic literature, betrothal is frequently referred to as sanctification (Hebrew: Kiddushin, קידושין), on account of the bride becoming "sanctified" (dedicated) to the groom.
The idea of erusin as the minimum necessary condition to apply the death penalty for adultery, but less than a complete marriage, appears in Deuteronomy.
A non-traditional view is that the betrothal was effected simply by purchasing the girl from her father (or guardian). The price paid for her (bride price) is known by the Hebrew term mohar (מוהר). The girl's consent is not explicitly required by any statement in the Bible, neither is there explicit permission to ignore it. Yet, as the servant of Abraham was seeking a Bride for Isaac, and discovered Rebekah living in Haran, it should be noted that her father Bethuel, and her brother Laban, said, "Let us call the young woman and ask her." And they called Rebekah and said to her, "Will you go with this man?" She said, "I will go."(Genesis 24:57, 58) It was customary in biblical times for the bride to be given part of the mohar. Gradually it lost its original meaning, and the custom arose of giving the mohar entirely to the bride, rather than to her father.
The traditional commentators do not necessarily explain mohar this way. Rashi understands mohar as a form of ketubah, an agreement to pay a certain amount upon divorce, and Nachmanides understands it as sovlanut, a sort of dowry or engagement present. Rashi understands Rachel and Leah's complaint to Jacob ("we are considered strangers to him for he has sold us") as saying that it was not normal for a father to sell his daughters, at least not without also giving them a dowry.