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. 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.
brokeness brings forth unknown beauty; untouched the shells of the lost; while stubborn, selfish mankind still ready to be cast in costs; as the crown of all creation, a princeless bride confused and scattered but hiding the sickness inside