What English does with the same spelling
Hide is first a verb: to put a thing out of sight, to keep a fact from view, or to stay unseen yourself. The same letters also name the thick skin of a large animal, and in British English a screened shelter from which a watcher looks at birds or game. Those uses sit close together in the mind. English also keeps a third hide, now mainly a historian's word: an old unit of farmland. That last sense is a different inheritance that happened to coincide in form.
The origin of the word hide, as a verb of concealing, is native. It was not taken from French after the Norman Conquest. Old English already had hȳdan, used both with an object and without one: to conceal something, to hide oneself, to keep a thing safe, even to bury a corpse. Middle English continued it as hiden. First English use belongs to the Old English period, before the twelfth century.
A West Germanic verb
The verb is West Germanic stock. Reconstructions of the earlier form do not match in every detail. One path runs through a West Germanic *hudjan, with related verbs in Middle Dutch and Middle Low German. Another derives Old English hȳdan from Proto-West Germanic *huʀdijan and Proto-Germanic *huzdijaną, a formation linked to the Germanic noun for a hoard, goods stored away. Both accounts treat the English verb as inherited, not borrowed.
Further back, handbooks usually posit a Proto-Indo-European root meaning to cover or conceal, written *(s)keu- or *(s)kewH-, with an extended shape *keudh- or *(s)kewdʰ- behind Ancient Greek keúthō, to hide. Welsh cuddio belongs in the same group. Latin custos, a guard, is sometimes offered as a more distant relative; that connection is looser than the Greek one and is not beyond dispute.
The Old English verb was originally weak. In early Modern English the past participle still varied: hid and hidden both appear in the 1611 Authorized Version of the Bible. Present-day English settled on hid for the simple past and hidden as the usual participle, so the conjugation looks irregular even though the word is old native material.
Skin as a covering
The noun hide, the pelt of a large animal, is equally old in English. Old English hȳd meant a hide or a skin. It goes back to Proto-Germanic *hūdiz and has close relatives across the family: Old Norse huð, Dutch huid, Old High German hut, German Haut. Latin cutis, skin, is a standard cognate from the same covering root, which is why English cutaneous and cuticle belong with this noun even though they arrived through Latin, not through Old English.
Specialists treat the concealing verb and the skin noun as related at a prehistoric level. Skin covers a body; to hide is to cover from view. That shared idea of covering is the link, not a joke that English invented later. Informal usage still uses hide for a person's life or safety, as in saving one's own hide: a shift from the animal skin to the body that wears it. From the same noun, around 1825, a slang verb meaning to flog appeared: to hide someone is to beat their hide.
The British wildlife hide, a screened hut, is a sense of concealment rather than of leather. A noun for a place of concealment is recorded in English from the fourteenth century; the modern bird hide is that idea in a specialized setting.
An alliterative pair, hide nor hair, meaning not a trace, is recorded in Middle English in the early fifteenth century. An earlier pairing, hide ne hewe, skin and complexion, was already in use around 1200. The later formula kept the skin sense while adding hair as the other visible surface of a person or animal.
The farm unit with another pedigree
The agrarian hide is unrelated. Old English hid, earlier higid or hīgid, named a measure of land. It belongs with hiwan, members of a household, and hiwo, the master of a house. The deeper Germanic forms point to a family or household group, and beyond that to a Proto-Indo-European root *kei- or *ḱey- associated with lying down and, by extension, with people who share a dwelling. Latin civis, citizen, is often cited as a cousin from that root, not from the covering root.
The unit was the land thought enough to support one free family and its dependents. Figures cluster around 100 or 120 acres, sometimes as little as 60 if the soil was poor. Another working definition was as much as one plough could work in a year. Medieval Latin often rendered the term as familia, which preserves the household idea more clearly than any acre count. The word survives in historical writing and in hidage, a tax assessed on hides of land.
One spelling, two inheritances
Speakers now hear one sound and write one spelling. Behind it sit two native lines. The verb of concealing and the noun for animal skin grow from an old covering root and still feed everyday phrases. The farm hide grows from a word for household and has nothing to do with secrecy. The coincidence of form is English history, not a single story.
German Haut for skin, beside English hide, is a useful check: the same Germanic noun, later vowels that diverged, still the covering sense. The land measure has no such twin in that meaning. That split is the cleanest way to keep the homonyms apart.