ECDSA or Elliptic Curve Digital Signature Algorithm is a variant of the Digital Signature Algorithm (DSA) which uses elliptic-curve cryptography.
See also Trezor Cryptography
ECDSA in Bitcoin
ECDSA is used in Bitcoin to ensure that funds can only be spent by their rightful owners. Concepts related to ECDSA are private key, public key or transaction signature. Every Bitcoin address is a cryptographic hash of an ECDSA public key.