Digital Signature
Formal
The signature is used to verify that the person who sends a particular transaction is, in fact, the owner of that wallet. It guarantees the contents of a message have not been altered in transit.
Practical
The signature is used to verify that the person who sends a particular transaction is in fact the owner of that wallet. This is done by including a message with the transaction so that the recipient can verify using the sendes public key. This way, the recipient can be sure that only the sender could have sent this message.
