When we say that someone or something is in between two other people or things, we mentally place them in the middle, with something on either side. After all, between refers to that space in the middle, right?
It does—but it hasn't always. The Old English word that eventually became between is actually made up of two parts: the prefix be- and the word twēonum. Twēonum is related to twā, the Old English word that gave us "two"; it's the dative plural form of an old distributive numeral that might be best translated as "two each." You'd expect that be- would mean "in," but it doesn't: betwēonum is literally "near two each." In its earliest uses, it wasn't always in reference to the intermediary position of two places, things, or people. It was also used to express reciprocal action by two people towards each other.
Though some claim that in between is redundant, we have evidence of it going back to at least the 1500s, if not earlier—one of our early uses notes that "The Sea brake in between Wisbich, and Walsockenne." The collocation was so common, in fact, that it eventually gave rise to the hyphenated in-between, a noun that refers to an intermediary.