Schnorr signatures, named after its inventor Claus-Peter Schnorr are another form of digital signatures. The signatures are based on the same security assumptions as ECDSA and are compatible with the elliptic curve Grin is using (secp256k1).
Light reading about Schnorr: https://hackernoon.com/a-brief-intro-to-bitcoin-schnorr-multi-signatures-b9ef052374c5
First discussion to implement in Grin: https://lists.launchpad.net/mimblewimble/msg00090.html
Github discussion and implementation of the signature scheme in Grin: https://github.com/mimblewimble/grin/issues/399
Expanding on the implementation: https://github.com/mimblewimble/grin/issues/1423
First proposal for the signature scheme in Bitcoin: https://eprint.iacr.org/2018/068.pdf
Implementation proposal in Bitcoin: https://github.com/sipa/bips/blob/bip-schnorr/bip-schnorr.mediawiki