Problem: 

Data Integrity "How to ensure that any modification to electronic data can be detected by the recipient of the data?"

Solution:

Data authentication appends a uniquely associated "TAG" to the data so that the recipient can verify the tag to ensure no modifications.

Problem: 

Sender Impersonation "How to authenticate data and identify the sender?"

Solution:

By use of Digital Signatures which append a uniquely associated signature to the data that can only be generated by the sender and cannot be forged.