Private key is an integer between 1 and roughly 2^256 — a number so large that picking one at random is, in practice, indistinguishable from picking a number no one else has ever picked. It is the only thing that authorizes a transaction from your address. Lose it and you lose the funds. Leak it and someone else takes the funds.
Where it actually lives
The private key never appears on chain. It is not "registered" with Bitcoin or Ethereum. Your wallet generates it locally the first time you set up: the device's random-number generator picks the number, computes the corresponding public key, then derives an address from the public key. The address is what the world sees; the private key stays on your device.
This is the central design choice that makes crypto self-custody possible — and the same design choice that makes it irreversible when something goes wrong.
Why "your keys" matters
The phrase "not your keys, not your coins" is shorthand for the consequence: if a third party holds the private key, that third party can move the funds without consulting you. Mt. Gox in 2014, Celsius in 2022, FTX in 2022 — three of the largest custody failures in crypto history were all the same shape: customer coins held under exchange-controlled private keys, which the exchange could and did move for purposes other than what customers expected.
Forms you'll encounter
Most US holders never see the raw 64-character hexadecimal key. The wallet hides it behind one of three abstractions: a twelve or twenty-four-word mnemonic phrase, a hardware-wallet device that holds the key in a secure element and signs transactions on-device, or — on enterprise setups — a multi-party computation scheme that never reconstructs the full key in one place.
The IRS angle
For US-resident holders, the IRS treats crypto as property (Notice 2014-21). Moving coins between your own addresses is not a taxable event, but the IRS expects records that prove you control both ends. Keep a clean cost-basis log alongside (not inside) your key backup — losing the log is not catastrophic but losing the key is.
Further reading: Private keys and mnemonic, Key-leak emergency rescue, Cold wallet.