secp256k1 is defined in SEC 2 over the prime p = 2^256 − 2^32 − 977 with a = 0 and b = 7. Its prime-order group gives about 128 bits of security, and a = 0 together with p ≡ 1 (mod 3) provides the GLV endomorphism that speeds up scalar multiplication. Unlike the NIST curves, its parameters were chosen for efficiency rather than derived from a seed.
Bitcoin adopted it in 2009 for ECDSA, and BIP 340 (Taproot) added Schnorr signatures on the same curve; Ethereum signs transactions and messages with it, and Nostr events carry BIP 340 Schnorr signatures. Ethereum (since EIP-2) and Bitcoin's relay policy reject the high-s form of ECDSA signatures to rule out malleability — see low-s.
Outside blockchains it is uncommon: RFC 8422 deprecated it for TLS (code point 22), JOSE (ES256K, RFC 8812) and COSE (algorithm −47) register it, and NIST SP 800-186 allows it only for blockchain-related applications.