ECDSA (Elliptic Curve Digital Signature Algorithm) was Bitcoin's original signature scheme. It uses the secp256k1 curve.
A signature proves you hold the private key without revealing it. Wallets now create the random part of each signature deterministically (RFC 6979), which avoids the risk of a weak random number leaking your key. Taproot added schnorr signatures alongside ECDSA.
Takeaway: ECDSA is the math that says "only the owner can spend".