Schnorr Signatures are an enhanced digital signature algorithm which brings multiple improvements over the traditional ECDSA signatures used in many cryptocurrencies.
Many of these improvements are around size, and privacy. Some examples of the improvements are...
Signature size is always the same, regardless of how many participants are involved - which in turn, leads to less information about the transaction leaking and improved privacy.
Reduced signature size, which leads to smaller transactions and more transactions per block.
Malleability fix. When Schnorr Signatures are fully adopted, transactions are no longer malleable which allow for advanced second layer solutions to built upon the network.
Schnorr Signatures were enabled on the Bitcoin Cash (BCH) network during the scheduled May 2019 hardfork.
* All terms and definitions may update as the Cryptionary improves.