To divide, separate, or make a distinction. Used of God separating light from darkness at creation, of the Levites being set apart for service, and of Israel being separated from the nations for holiness.
Badal is one of the most theologically loaded verbs in the Old Testament. It appears first in Genesis 1 where God 'separates' light from darkness — separation is the grammar of creation, the means by which order emerges from chaos. This same verb describes the priestly calling: Levites were 'separated' (badal) for service (Numbers 8:14), and Israel's holiness: 'I have set you apart from the nations to be my own' (Leviticus 20:26). To be holy is to be separated.