Abarim Publications' online Biblical Hebrew Dictionary
The root-verb בין (bin) means to understand (Job 18:2), consider (Deuteronomy 32:7), perceive (Proverbs 7:7), have insight (Jeremiah 49:7), discern (1 Samuel 16:18). In Arabic this word means to become separated. In Sabean an associated noun means the wise.
Two derivatives of this verb are בינה (bina) and תבונה (tebuna), both meaning understanding, which is quite logical, but derivative בין (ben) meaning 'between' is perhaps harder to distinguish.
A radar works by emitting bundles of rays. If the bundle is wide, two little objects in the distance will be reflected as one dot on the radar screen. If the bundle is narrow the two little objects will be separately distinguished.
This difficult adverb therefore primarily defines the identity of parties and their relative identity, rather than just the space between them. This is the reason why this word occurs double or triple in statements like: ביני וביניכם ובין כל־נפש חיה, literally: between me and between you and between all living breathers (Genesis 9:12).
The dual form of this word is בנים (benim), and denotes the space between two armies (1 Samuel 17:4). Note that this dual form is spelled the same as בנים (benim), the plural of בן (ben), meaning son. The feminine form of בין (ben) is בית (byt).