When sending a Bitcoin transaction, the amount to be sent is calculated by receiving from the blockchain the total unspent Bitcoin amounts you received previously. Each of the inputs demands its own signature under the current Elliptic Curve Digital Signature Algorithm. That increased the size of the transaction, and thus, its fee.
Schnorr signatures are the most efficient way to store signature data in transactions. When utilizing Schnorr algorithm, all inputs are accumulated and stored as one signature. It saves transaction space significantly, and allows increasing transaction capacity, while blocks store more transactions at an average.
Schnorr signatures can also benefit CoinJoin transactions, and thus, can help Bitcoin’s advancement in privacy. It unites transaction inputs with transactions of other people, when they make payments to receiver. When they are united like that, it’s difficult to track which of the users sent which input, they are totally anonymous. CoinJoin transactions have raised fees because of higher inputs number in one transaction, what resulted in a higher signatures number. Using Schnorr signatures would allow all signatures in one transaction to be squeezed into one, saving on transaction fees and contributing to CoinJoin usage. Moreover, Schnorrlays the ground for multisig transactions, what requires signing off multiple parties. The number of parties’ signatures doesn’t matter in that case, while the Schnorr signature is all the transaction needs.