"rabbit-hole, fox-hole, hole in the ground excavated by an animal as a refuge or habitation," c. 1300, borewe, a collateral form of Old English burgh "stronghold, fortress" (see borough); influenced by bergh "hill" and berwen "to defend, take refuge."
c. 1600, "to place in a burrow," from burrow (n.). Figuratively (such as to burrow (one's) head) by 1862. Intransitive sense, "to bore one's way into, penetrate, make a hole in" is from 1610s, originally figurative; the literal sense, of animals, is attested by 1771. Related: Burrowed; borrowing.